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Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity

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... Background Spacetime distortions have long been a subject of theoretical interest in physics, with applications ranging from general relativity to quantum field theory. Albert Einstein's theory of general relativity first introduced the idea that massive objects distort the fabric of spacetime, producing phenomena such as gravitational lensing and black hole event horizons (Weinberg, 1972). More recently, theoretical models have expanded the concept of spacetime distortions to include localized, controllable phenomena such as warp bubbles. ...
... , This shows that the bubble's total energy is proportional to the peak energy density and the spatial width , further highlighting the importance of energy localization (Weinberg, 1972). ...
... , Where is the radial distance from the bubble center (Weinberg, 1972), for a trajectory grazing the bubble at a distance , the deflection angle is derived by integrating the geodesic equation: ...
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This paper develops a comprehensive theoretical framework for nano warp bubbles localized distortions in spacetime that hold the potential to transform our understanding of quantum gravity, spacetime topology, and advanced technologies. These bubbles are conceptualized as emergent phenomena within a unified model integrating the Dodecahedron Linear String Field Hypothesis (DLSFH) and Geometric Quantum Realism (GQR). The DLSFH introduces a discrete, dodecahedral geometry for spacetime, providing the structural and topological foundation for particle interactions and localized curvature. GQR complements this by proposing quantized spacetime curvature, resolving infinities in quantum field theory, and providing a natural framework for localized spacetime distortions. Mathematical models are developed to describe the formation, stability, and behavior of nano warp bubbles, highlighting energy thresholds, resonance conditions, and quantized curvature eigenstates. The energy required to form these bubbles is shown to depend on the quantization scale of spacetime, while the dodecahedral symmetries of the spacetime lattice govern their stability. Observable effects such as localized gravitational lensing, variations in quantum field interactions, and gravitational wave modulations are proposed as experimental signatures of these phenomena. The potential applications of nano warp bubbles are significant and far-reaching. In propulsion systems, they could form the basis for scalable warp drives by enabling localized spacetime contractions and expansions. In energy systems, the bubbles' ability to confine high energy densities offers novel methods for compact energy storage and lossless transfer. Furthermore, their use in quantum communication could enable faster-than-light information transfer by exploiting spacetime shortcuts while preserving quantum coherence. This study bridges gaps in current theoretical physics by integrating quantum geometry and spacetime quantization to describe and predict nanoscale spacetime distortions. By proposing testable predictions and practical applications, it provides a foundation for future experimental investigations and technological innovations in quantum gravity, energy systems, and propulsion technologies.
... While both frameworks have been experimentally validated to remarkable precision, they are fundamentally incompatible when applied together. This incompatibility is particularly evident in extreme conditions, such as inside black holes or during the early moments of the universe, where quantum gravitational effects are expected to dominate (Weinberg, 1972). ...
... Unlike the spacetime of general relativity, which is dynamically curved by the presence of matter and energy, hyperspace is envisioned as a pre-existing structure that provides the stage for the emergence of spacetime itself. This construct is motivated by the limitations of standard 4-dimensional spacetime in explaining phenomena such as quantum entanglement, the unification of forces, and the reconciliation of quantum mechanics with general relativity (Weinberg, 1972). Hyperspace, as proposed here, offers additional dimensions that accommodate these complexities while remaining mathematically consistent with known physical laws. ...
... 2. Unification of Forces: Hyperspace serves as the stage for unifying the fundamental forces of nature. When projected onto four-dimensional spacetime, strong and electroweak interactions can be described as different manifestations of a single higher-dimensional force (Weinberg, 1972;Polchinski, 1998). ...
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The quest to unify quantum mechanics and general relativity remains one of the most profound challenges in theoretical physics. This paper introduces a novel framework for a Theory of Everything (ToE), built upon a hierarchical model that incorporates hyperspace, the superluminal graviton condensate vacuum (SGCV), the zero-point energy (ZPE) field, and Standard Model (SM) particles as emergent phenomena. In this model, hyperspace is conceptualized as a higher-dimensional geometric structure, the "empty room," which provides the foundation for all physical interactions. The SGCV, analogous to the "air" within this room, represents a superluminal condensate of gravitons that underpins the fabric of spacetime and facilitates gravitational interactions. From the SGCV, the ZPE field emerges as "vapor," a quantum fluctuation-driven medium that gives rise to energy density throughout the universe. Finally, SM particles manifest as "vapor manifolds," localized excitations within the ZPE field that derive their properties from interactions with the SGCV and hyperspace geometry. This model offers a layered approach to unifying quantum mechanics and general relativity by embedding both within the dynamic interplay of hyperspace, SGCV, and ZPE. Key features include a mechanism for the emergence of spacetime curvature from the SGCV medium and a description of particle masses and interactions as topological features of the underlying quantum vacuum. The paper further explores how this framework aligns with experimental efforts at CERN and LIGO. At CERN, high-energy particle collisions could provide evidence of SGCV evaporation or deviations in Higgs boson decay channels. At LIGO, gravitational wave observations could reveal subtle modulations caused by interactions between gravitational waves and the SGCV medium. These connections underscore the testable nature of the proposed ToE model, bridging the gap between theoretical constructs and empirical data. By integrating these concepts into a unified framework, this ToE model advances our understanding of fundamental physics and provides a novel pathway toward resolving longstanding questions about the nature of spacetime, gravity, and quantum fields.
... The origin of mass in fundamental particles is a cornerstone of modern physics. While the Higgs mechanism explains the intrinsic masses of quarks through their interaction with the Higgs field (Aghanim et al., 2018), the majority of the mass of composite particles, such as protons and neutrons, arises from QCD binding energy (Weinberg, 1972). However, the potential role of quantum gravity effects, such as those involving quantum black holes, remains underexplored (Clifton et al., 2012). ...
... Despite the Higgs mechanism providing the masses of quarks, their combined contribution accounts for only a small fraction of the proton's total mass. The total proton mass is approximately , yet the summed mass of its constituent quarks (two up quarks and one down quark) is only about (Weinberg, 1972). This discrepancy is explained by Quantum Chromodynamics (QCD), where: ...
... Quantum Chromodynamics (QCD) is a quantum field theory that describes the strong interaction governing the behavior of quarks and gluons. As explained by Einstein's mass-energy equivalence (Weinberg, 1972), the majority of the mass of nucleons, such as protons and neutrons, arises from the binding energy of gluons and the kinetic energy of confined quarks. This energy results from the non-perturbative dynamics of QCD, which leads to the confinement of quarks within hadrons. ...
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Mass formation in subatomic particles, such as protons and neutrons, arises from an intricate interplay between the Higgs mechanism, quantum chromodynamics (QCD), and potentially quantum gravitational effects. This paper explores the hypothesis that quantum black holes and gravitational quantum resonance (GQR) contribute to mass generation, with the massive blue star Spica providing a unique astrophysical environment for observational validation. The Dodecahedron Linear String Field Hypothesis (DLSFH) offers a geometric framework to interpret quark arrangements and their interactions in Spica's intense gravitational and energetic field. By integrating DLSFH and GQR, this study proposes new methods to investigate the relationship between macroscopic astrophysical phenomena and micro-scale quantum mass formation (Valamontes, 2024).
... As well known, the gravitational deflection of light is one of the crucial predictions of the General Relativity (GR) and still plays a key role in understanding the problems related to Astronomy, Cosmology and Gravitational Physics [1]. ...
... In this section, we give the main equation of the null-geodesic motion in a spherical symmetry gravitational field in GR which are required to be solved for the deflection of light problem. The stationary line element of 4-dimensional general spherically symmetric spacetime in GR [1,8] can be represented by ...
... In the case of the Reissner-Nordström spacetime of a charged star, we have [1] f ...
Preprint
In this paper, the homotopy-perturbation method (HPM) is applied to obtain approximate analytical solutions for the gravitational deflection of light in General Relativity near Schwarzschild black hole surrounded by quintessence (Kiselev black hole). In order to demonstrate that HPM is able to yield acceptable solutions for the null-geodesics with easily computable terms, the HPM is tested for the simple examples of spherically symmetric spacetimes such as Schwarzschild and Reissner-Nordstr\"{o}m black holes. After that, the null-geodesics of light passing the vicinity of Kiselev black hole are studied via the HPM in two particular cases regarding the equation of state parameter of quintessence. In addition, a formula for the angle of deflection has been obtained via HPM in the form of a series which allows to calculate the angle with any accuracy without requirement of its smallness.
... On the other hand, in the present paper we introduce the formal kinetic theory definition of heat flux in the Navier-Stokes regime with no acceleration coupling, instead particle number density, temperature and gravitational potential gradients are present in the final expression, according to the assumptions of linear irreversible thermodynamics. Moreover, Wodarzik assumes that the fluid bulk moves following geodesics, argument that can be questioned as individual molecules follow geodesics [7], but stresses deviate the bulk from this type of dynamics. It is well known that the hydrodynamic velocity (U ν ) satisfies Euler equation [8,9]:ρU ...
... 2 Basic formalism: relativistic fluids 2.1 Basic elements of general relativity and the Schwarzschild metric A simple, non-degenerate gas is considered in a Riemaniann space where the line element (arc length) is generally expressed as [7,10]: ...
... On the other hand, in a general relativistic scenario,ḟ corresponds to the arc length derivative (ḟ = df ds ), with s being the arc length [7]. Also in this approach, we haveẋ ...
Preprint
Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \textquotedblleft suppressing\textquotedblright{} the molecular acceleration in Boltzmann\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
... Both for electromagnetism and gravity the relation between classical radiation and soft theorem at the leading order has been noted before, see e.g. [79] for electromagnetism and [85] for gravity. However this relation at the subleading and subsubleading order does not seem to have been explored in detail before. ...
... We can arrive at expression (4.6) by starting with (3.2) and performing the sum over polarizations before taking the M 0 → ∞ limit. This will give [85] ...
... In [85] Weinberg considered the situation where a bunch of particles moving along straight lines meet at a single point in space-time and come out as another bunch of particles emerging from the same space-time point and moving along straight line trajectories. Physically this corresponds to the situation where there is a repulsive short-range interaction between the particles where the range of the interaction is large compared to the Schwarzschild radii of the particles. ...
Preprint
Classical limit of multiple soft graviton theorem can be used to compute the angular power spectrum of long wavelength gravitational radiation in classical scattering provided the total energy carried away by the radiation is small compared to the energies of the scatterers. We could ensure this either by taking the limit in which the impact parameter is large compared to the Schwarzschild radii of the scatterers, or by taking the probe limit where one object (the probe) has mass much smaller than the other object (the scatterer). We compute the results to subsubleading order in soft momentum and test them using explicit examples involving classical scattering. Our analysis also generalizes to the case where there are multiple objects involved in the scattering and the objects exchange mass, fragment or fuse into each other during the scattering. A similar analysis can be carried out for soft photons to subleading order, reproducing standard textbook results. We also discuss the modification of soft expansion in four dimensions beyond the leading order due to infrared divergences.
... The General theory of Relativity (GR) [1,2] announced in 1915 was theoretically developed by A. Einstein, and it has been experimentally verified as an excellent theory of gravitation. In particular, the GR was once again a e-mail: anhky AT iop.vast.ac.vn b e-mail: phamkyvatly AT gmail.com ...
... c e-mail: nhvan AT iop.vast.ac.vn confirmed triumphantly by recent detections of gravitational waves (see, for example, [3,4]). The GR is governed by the Einstein equation [1,2,5] ...
... This equation can describe very well gravitational phenomena of the normal matter, but it ineffectively describes other phenomena such as the Universe's accelerated expansion (supposed to be explained by the introduction of the concept of the so-called dark energy or cosmological constant), dark matter, cosmic inflation, quantum gravity, etc. One of the simplest suggestions for solving the dark energy problem is adding the cosmological constant Λ to the Lagrangian, that is, L G = R−2Λ, leading to the equation of motion [1,5] f (R), where f (R) is a scalar function of the scalar curvature R. The equation of motion now becomes [7][8][9] f (R)R µν − g µν f (R) ...
Preprint
Exact solutions of an f(R) -theory (of gravity) in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a non-static central field are not easy at all. There are, however, approximation methods of finding a solution in a central field which is not necessarily static. It is shown in this article that an approximate solution of an f(R)-theory in a general central field, which is not necessary to be static, can be found perturbatively around a solution of the Einstein equation in the general theory of relativity. In particular, vacuum solutions are found for f(R) of general and some special forms. Further, applications to the investigation of a planetary motion and light's propagation in a central field are presented. An effect of an f(R)-gravity is also estimated for the SgrA*--S2 system. The latter gravitational system is much stronger than the Sun--Mercury system, thus the effect could be much stronger and, thus, much more measurable.
... For this particular case, this primitive variable set is given by by the pressure p, the velocity along three spacial dimensions v i and, the particle number density n 1 . In here and in what follows all thermodynamical quantities (pressure p, particle number density n and energy density e and so on, are measured on its proper reference frame following the convention by [3,4]). The explicit dependences q = q(u(x, t)) and f = f (u(x, t)) for 1D flow in the special relativistic case are given by (see e.g. ...
... The explicit dependences q = q(u(x, t)) and f = f (u(x, t)) for 1D flow in the special relativistic case are given by (see e.g. [3,4]): ...
... From this point onwards, we are going to use f (x, t) instead of the cumbersome notation f (q(u(x, t))), bearing in mind that both, charges and flux vectors, depend on the primitive variables u(x, t).4 In equation (A3), the derivative ∂fa/∂x at a given time tn was written using a central approximation value given by (fa(x i+1 ) − fa(x i−1 ))/(2∆x). ...
Preprint
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.
... The advance of the perihelion in the orbit of Mercury is a relativistic effect [1]. Together with the observation of the deflection of light, this result offers unique possibilities for testing General Relativity (GR) and exploring the limits of alternative theories of gravitation. ...
... As well known [1,3], the line element of the 4dimensional general spherically symmetric stationary spacetime can be written as ...
... Finally, let us obtain the HPM orbits and shift in the Reissner-Nordstorm spacetime of a charged star. In this case, we have [1] ...
Preprint
We propose a new approach in studying the planetary orbits and the perihelion precession in General Relativity by means of the Homotopy Perturbation Method (HPM).For this purpose, we give a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime which are to be studied in our work. On the basis of the main idea of HPM, we construct the appropriate homotopy what leads to the problem of solving the set of linear equations. First of all, we consider the simple example of the Schwarzschild metric for which the approximate geodesics solutions are known, in order to compare the HPM solution for orbits with those obtained earlier. Moreover, we obtain an approximate HPM solution for the Reissner-Nordstorm spacetime of a charged star.
... This procedure fails if one wishes to describe the dynamics of a fluid with viscosity interacting with gravity in that the classical Navier-Stokes equations are not known to be the Euler-Lagrange equations of a specific action functional. While this does not prevent us from writing a stress energy-tensor for the Navier-Stokes equations, its generalization to general relativity is not unique, and, in fact, presents ambiguities [111]. A review of some of the different proposals for handling viscosity in relativity is given in section 3. Section 3 also discusses similarities and differences between the the approach studied in this paper and other theories of relativistic viscosity. ...
... Even with these inconsistencies, the Eckart theory was nonetheless used, fully or partially, with different degrees of success, in the study of neutron stars, supernovae, and in some models of viscous cosmology. Without being exhaustive, we provide the following list of references to this important topic: [3,5,6,7,8,9,11,12,20,28,29,30,31,32,39,40,41,42,43,45,47,48,49,50,51,52,53,62,64,70,76,77,78,82,85,86,88,89,90,91,92,94,97,98,101,102,104,106,107,108,110,111,113]. ...
... While such a choice is widely used in the literature of relativistic viscous fluids, one has to be aware that it is a choice, but one which nonetheless does not seem a priori better motivated than the use of u L . We refer the reader to [98,111] for more details. ...
Preprint
We consider a first order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation of state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged non-linear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach here explored and other theories of relativistic viscosity, including the Mueller-Israel-Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. Finally, it is also shown how the present model can be generalized to a second order formulation.
... In the Newtonian theory, energy is a well-defined quantity and is conserved along physical trajectories (barring friction), which ensures the existence of a scalar potential for the gravitational force. In General Relativity [1], the very concept of energy becomes much more problematic (see, e.g. [2] and References therein) and there is no invariant notion of a scalar potential. ...
... For an arbitrary matter density, it is hopeless to solve the equation (2.25) for V (1) analytically. Let us then consider the very simple case in which ρ is uniform inside a sphere of radius R, For this matter density, we shall now solve Eqs. ...
... This is precisely the expression following from the isotropic form of the Schwarzschild metric [1], and the one we will consider as our reference term throughout this paper. ...
Preprint
We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order. We start by obtaining a Lagrangian for the gravitational potential coupled to a static matter source from the weak field expansion of the Einstein-Hilbert action. By analysing a few classical solutions of the resulting field equation, we show that our construction leads to the expected post-Newtonian expressions. Next, we show that one can reproduce the classical Newtonian results very accurately by employing a coherent quantum state and modifications to include the first post-Newtonian corrections are considered. Our findings establish a connection between the corpuscular model of black holes and post-Newtonian gravity, and set the stage for further investigations of these quantum models.
... In this section, we offer a derivation of such equations, inspired by Refs. [14][15][16][17][18][19][20][21]. In the following sections, we apply them to cosmology and stellar equilibrium and compare their predictions with those from GR and from the Neo-Newtonian theory. ...
... It is useful to maintain explicit the presence of the speed of light c, in order to perform a post-Newtonian analysis, see e.g. [21]. Let's also consider a perfect fluid with pressure p, energy density ρc 2 and 4-velocity u µ . ...
... The Einstein tensor components are easily calculated from metric (2.1) and are the following, to the lowest order in the 1/c expansion (see also [21]): ...
Preprint
We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate i) the cosmological expansion, ii) linear cosmological perturbations theory and iii) stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General Relativity theory. We show that the predictions for the background evolution of the Universe are deeply changed with respect to the General Relativity theory: the acceleration of the Universe is achieved with positive pressure. On the other hand, the behaviour of small cosmological perturbations reproduces the one found in the relativistic context, even if only at small scales. We argue that this last result may open new possibilities for numerical simulations for structure formation in the Universe. Finally, the properties of neutron stars are qualitatively reproduced by Hwang-Noh equations, but the upper mass limit is at least one order of magnitude higher than the one obtained in General Relativity.
... (2) are invariant under de Sitter group SO(1, 4). The metric of this space-time can be written as [15] ...
... where µ, ν = 0, ..., 3, K = 1 R 2 = Λ 3 , Λ is the cosmological constant. This metric is invariant under two classes of simple transformations (see, for example, P 387 of the book [15]), one is SO(1, 3) transformations: ...
... and A a are components of the 'ordinary' vector [15]. This vector is that what we are seeking for, i.e. the observable vector. ...
Preprint
We propose an effective Lorentz violating electrodynamics model via static de Sitter metric which is deviated from Minkowski metric by a minuscule amount depending on the cosmological constant. We obtain the electromagnetic field equations via the vierbein decomposition of the tensors. In addition, as an application of the electromagnetic field equations obtained, we get the solutions of electrostatic field and magnetostatic field due to a point charge and a circle current respectively and discussed the implication of the effect of Lorentz violation in our electromagnetic theory.
... where R r represents the radius of the resonance surface, while the value of δ depends on the proto-NS model, such as the polytropic [51][52][53][54] or spherical Eddington models [55]. However, in this scenario, a magnetic field on the order of 10 16 G and a neutrino mass around 100 eV are required. ...
... • The polytropic model: The isotropic neutrinosphere in the polytropic model is described by the following equations [51][52][53][54] dP(r) ...
Article
Full-text available
The high speeds seen in rapidly rotating pulsars after supernova explosions present a longstanding puzzle in astrophysics. Numerous theories have been suggested over the years to explain this sudden "kick" imparted to the neutron star, yet each comes with its own set of challenges and limitations. Key explanations for pulsar kicks include hydrodynamic instabilities in supernovae, anisotropic neutrino emission, asymmetries in the magnetic field, binary system disruption, and physics beyond the Standard Model. Unraveling the origins of pulsar kicks not only enhances our understanding of supernova mechanisms but also opens up possibilities for exploring new physics. In this brief review, we will introduce pulsar kicks, examine the leading hypotheses, and explore future directions for this intriguing phenomenon.
... Although the heat conduction and bulk viscosity do not affect the evolution of GWs as far as we consider the linear order in perturbation theory, the existence of shear viscosity (parameterized by the shear viscosity coefficient η) modifies the propagation equation of GWs. In the flat FRW universe, we have [42] ...
... 3 In contrast to the shear viscosity, the bulk viscosity does not modify the propagation of GWs, but it modifies the equation for the background expansion [i.e. the evolution of the scale factor a(t)]. In the FRW universe, the effect of the bulk viscosity (parameterized by the bulk viscosity coefficient ζ) is described by making the following replacement for the pressure [42], ...
Preprint
In this paper, we revisit the estimation of the spectrum of primordial gravitational waves originated from inflation, particularly focusing on the effect of thermodynamics in the Standard Model of particle physics. By collecting recent results of perturbative and non-perturbative analysis of thermodynamic quantities in the Standard Model, we obtain the effective degrees of freedom including the corrections due to non-trivial interaction properties of particles in the Standard Model for a wide temperature interval. The impact of such corrections on the spectrum of primordial gravitational waves as well as the damping effect due to free-streaming particles is investigated by numerically solving the evolution equation of tensor perturbations in the expanding universe. It is shown that the reevaluation of the effects of free-streaming photons and neutrinos gives rise to some additional damping features overlooked in previous studies. We also observe that the continuous nature of the QCD crossover results in a smooth spectrum for modes that reenter the horizon at around the epoch of the QCD phase transition. Furthermore, we explicitly show that the values of the effective degrees of freedom remain smaller than the commonly used value 106.75 even at temperature much higher than the critical temperature of the electroweak crossover, and that the amplitude of primordial gravitational waves at a frequency range relevant to direct detection experiments becomes O(1)%\mathcal{O}(1)\,\% larger than previous estimates that do not include such corrections. This effect can be relevant to future high-sensitivity gravitational wave experiments such as ultimate DECIGO. Our results on the temperature evolution of the effective degrees of freedom are made available as tabulated data and fitting functions, which can also be used in the analysis of other cosmological relics.
... This requirement ensures that F is gauge-invariant, since these constraints are the generators of the gauge transformations. Indeed we recall that {Φ a , F } ≡ −i Va dF where V a is the vector field associated with Φ a , so if (11) holds then i Va dF | P = 0 (12) and hence F is unaffected by gauge transformations. ...
... The only way around this problem would be to evaluate local invariants at space-time points that are identified in a diffeomorphism-invariant manner; for example, as the points at which certain local invariants take specified values. However, this approach does not appear to work in the case of pure gravity, since at each point there are only 4 algebraically independent local invariants (all obtained from the Weyl tensor C µνρσ [12]). Hence, even if a point could be identified as the unique location where these 4 quantities took specified values, there would be no remaining independent local invariants to measure there. ...
Preprint
In the canonical approach to general relativity it is customary to parametrize the phase space by initial data on spacelike hypersurfaces. However, if one seeks a theory dealing with observations that can be made by a single localized observer, it is natural to use a different description of the phase space. This results in a different set of Dirac observables from that appearing in the conventional formulation. It also suggests a possible solution to the problem of time, which has been one of the obstacles to the development of a satisfactory quantum theory of gravity.
... In order to shed light on the effects of the non-conservation on the geometrical side of the field equation (25) when λ µ = 0, it is interesting to investigate the behavior of gravitational waves. We suppose the metric to be close to the Minkowski one [5], i.e. g µν = η µν + h µν with |h µν | ≪ 1. To first order in h, by choosing the modified harmonic gauge η µν (h µρ,ν − 1 2 h µν,ρ + λ µ h νρ − 1 2 λ ρ h µν ) = 0, we obtain from the field equations ...
... Furthermore, as the metric should be a smooth function of time, we can estimate an upper limit of only |∆θ λ − ∆θ 0 | 10 −7 seconds of arc per century for the difference between the Mercury precession ∆θ λ in our theory (with |λ 0 |c ≈ 10 −10 ) and the precession of ∆θ 0 = 43.03 ′′ per century in classical gravity [5]. ...
Preprint
In the present work, we propose an Action Principle for Action-dependent Lagrangians by generalizing the Herglotz variational problem for several independent variables. This Action Principle enables us to formulate Lagrangian densities for non-conservative fields. In special, from a Lagrangian depending linearly on the Action, we obtain a generalized Einstein's field equations for a non-conservative gravity and analyze some consequences of their solutions to cosmology and gravitational waves. We show that the non-conservative part of the field equations depends on a constant cosmological four-vector. Depending on this four-vector, the theory displays damped/amplified gravitational waves and an accelerating Universe without dark energy.
... cently advocated breaking of the BMS symmetry [6] precisely induced by the presence of localised matter. Our main result is that these (soft off-shell) gravitons satisfy Bekenstein's area law [7] and appear to produce the expected post-Newtonian correction [8] to the total energy of the system, which becomes a major contribution to the dynamics when the gravitational radius is approached. At that point, a black hole should form, mostly made of such soft gravitons (in a sense that will be clarified later on), in qualitative agreement with the corpuscular model of Refs. ...
... which we note is positive and falls off with the size R of the source like 1/R 2 , two properties that characterise a typical post-Newtonian correction to the Newtonian potential [8]. Since ...
Preprint
We consider the effects of gravitons in the collapse of baryonic matter that forms a black hole. We first note that the effective number of (soft off-shell) gravitons that account for the (negative) Newtonian potential energy generated by the baryons is conserved and always in agreement with Bekenstein's area law of black holes. Moreover, their (positive) interaction energy reproduces the expected post-Newtonian correction and becomes of the order of the total ADM mass of the system when the size of the collapsing object approaches its gravitational radius. This result supports a scenario in which the gravitational collapse of regular baryonic matter produces a corpuscular black hole without central singularity, in which both gravitons and baryons are marginally bound and form a Bose-Einstein condensate at the critical point. The Hawking emission of baryons and gravitons is then described by the quantum depletion of the condensate and we show the two energy fluxes are comparable, albeit negligibly small on astrophysical scales.
... In addition to the spherical symmetry we also require the static condition, such that all the fields are timeindependent, ∂ t ≡ 0. By utilizing ordinary diffeomorphisms we can set g tr ≡ 0 [26], and hence without loss of generality we can put the Riemannian metric into the diagonal form [24] ds 2 = e 2φ(r) −A(r)dt 2 + A −1 (r)dr 2 + A −1 (r)C(r) dΩ 2 , ...
... Furthermore, without loss of generality, we can put g tr = 0, g ϑϑ = r 2 , and set the metric to be diagonal, utilizing diffeomorphisms (see e.g. [26]), ds 2 = −B(r)dt 2 + A(r)dr 2 + r 2 dΩ 2 , (A. 29) where we put as shorthand notation, dΩ 2 := dϑ 2 + sin 2 ϑ dϕ 2 . ...
Preprint
Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an O(D,D)\mathrm{O}(D,D) covariant differential geometry beyond Riemann, we spell out the definition of the Energy-Momentum tensor in Stringy Gravity and derive its on-shell conservation law from doubled general covariance. Equating it with the recently identified stringy Einstein curvature tensor, all the equations of motion of the closed string massless sector are unified into a single expression, GAB=8πGTABG_{AB}=8\pi G T_{AB}, which we dub the `Einstein Double Field Equations'. As an example, we study the most general D=4{D=4} static, asymptotically flat, spherically symmetric, `regular' solution, sourced by the stringy Energy-Momentum tensor which is nontrivial only up to a finite radius from the center. Outside this radius, the solution matches the known vacuum geometry which has four constant parameters. We express these as volume integrals of the interior stringy Energy-Momentum tensor and discuss relevant energy conditions.
... Indeed, it is well-known that there are no representations of the group GL(4, R) of the automorphisms of R 4 which behave like spinors under the subgroup of Lorentz transformations. Therefore, if one aims at considering the coupling between general relativity and fermionic fields, one is forced to resort to the so-called "tetrad formalism" (cf., e.g., [47]). Yet, there seems to have been a widespread misunderstanding of the full mathematical (and physical) significance of this. ...
... Note that, although the invariance of the Dirac Lagrangian with respect to Lorentz transformations requires θ T ab to be symmetric on shell [47,6], the manipulation required for going from (5.15) to (5.16) is highly non-trivial: the interested reader is referred to [31] for an elegant proof. Following the same procedure as before, we find that the Noether current associated with θ L is ...
Preprint
We present a clear-cut example of the importance of the functorial approach of gauge-natural bundles and the general theory of Lie derivatives for classical field theory, where the sole correct geometrical formulation of Einstein (-Cartan) gravity coupled with Dirac fields gives rise to an unexpected indeterminacy in the concept of conserved quantities.
... A nice presentation of the KL mechanism can be found in [27]. An introduction to PN precession can be found in any standard textbook of general relativity, e.g., [35]. Finally, the back reaction of GW emission on an elliptic binary orbit was firstly studied in [39]. ...
... As is well known, the first nontrivial order of the PN correction to the Keplerian potential is a trivial constant shift plus a new term proportional to the inverse square of the distance, for which the net effect is to generate a precession for the periapsis of an elliptical orbit. The precession rate is given by (See, e.g., [35]), ...
Preprint
With better statistics and precision, eccentricity could prove to be a useful tool for understanding the origin and environment of binary black holes. Hierarchical triples in particular, which might be abundant in globular clusters and galactic nuclei, could generate observably large eccentricity at LIGO and future gravitational wave detectors. Measuring the eccentricity distribution accurately could help us probe the background and the formation of the mergers. In this paper we continue our previous investigation and improve our semi-analytical description of the eccentricity distribution of mergers hierarchical triple systems. Our result, which further reduces the reliance on numerical simulations, could be useful for statistically distinguishing different formation channels of observed binary mergers.
... where dp and dt are calculated in the same frame (any frame), but F is calculated in the frame comoving with the particle (see e.g. Weinberg, 1972). Since we assume that the layer and the spine are optically thin, we can calculate the motion of a single particle due to Compton scattering. ...
... Since the spine is active between points that are fixed in the observer frame K, it is easier to compute the integral in that frame K. From the relations of aberration of the light (e.g. Weinberg, 1972) we have useful transformations: ...
Preprint
It has been proposed that blazar jets are structured, with a fast spine surrounded by a slower sheath or layer. This structured jet model explains some properties of their emission and morphology. Because of their relative motion, the radiation produced by one component is seen amplified by the other, thus enhancing the inverse Compton emission of both. Radiation is emitted anisotropically in the comoving frames, and causes the emitting plasma to recoil. As seen in the observer frame, this corresponds to a deceleration of the fastest component (the spine) and an acceleration of the slower one (the layer). While the deceleration of the spine has already been investigated, here we study for the first time the acceleration of the sheath and find self-consistent velocity profile solutions for both the spine and the sheath while accounting for radiative cooling. We find that the sheath can be accelerated to the velocities required by the observations if its leptons remain energetic in the acceleration region, assumed to be of the order of 100 Schwarzschild radii, demanding continuous injection of energetic particles in that region.
... However, differently from the fictitious force in Newton's dynamics, ω is here a physical field to be treated on the same footing as g. In particular, ω is the antisymmetric part of the gravitational field that is left behind from the limit λ → 0 and that is not necessarily subdominant with respect to g, as is the case in a standard post-Newtonian expansion [37]. ...
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Ehlers' Frame Theory is a class of geometric theories parameterized by λ := 1/c 2 and identical to the General Theory of Relativity for λ = 0. The limit λ → 0 does not recover Newtonian gravity, as one might expect, but yields the so-called Newton-Cartan theory of gravity, which is characterized by a second gravitational field ω, called the Coriolis field. Such a field encodes at a non-relativistic level the dragging feature of general spacetimes, as we show clearly for the case of the (η, H) geometries. Taking advantage of the Coriolis field, we apply Ehlers' theory to an axially symmetric distribution of matter, mimicking, for example, a disc galaxy, and show how its dynamics might reproduce a flattish rotation curve. In the same setting, we further exploit the formal simplicity of Ehlers' formalism in addressing non-stationary cases, which are remarkably difficult to be treated in the General Theory of Relativity. We show that the time derivative of the Coriolis field gives rise to a tangential acceleration which allows to study a possible formation in time of the rotation curve's flattish feature.
... entangling gravitons Alice's state emits during her experiment. We treat the components of her state as point-like particles such that the stress-energy of the i th component is [8] T ab ...
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In this work, we study the decoherence of a quantum spatial superposition of a massive body created by an observer, Alice, that is subject to a short burst of gravitational radiation. We consider gravitational wave bursts with a simple oscillatory waveform and step-function memory waveform. Using a local description of the decoherence, we obtain an analytic estimate of the number of soft gravitons radiated by Alice's state. Moreover, we decompose her decoherence into contributions from the oscillatory and memory waveforms. We show that Alice's state decoheres proportional to the memory of the gravitational radiation she emits. To leading order, our calculation using a local description of the decoherence agrees with the decoherence caused by her radiating quadrupole. In general, the oscillatory contributions are strongly dependent on the phase of the burst when it is switched off. This work serves as a step towards understanding the interplay between quantum mechanical systems and gravity by demonstrating the role gravitational waves and the memory effect have in the loss of coherence of quantum superpositions. We also briefly investigate the electromagnetic analogue of this gedankenexperiment, in which Alice is subject to a burst of electromagnetic radiation, and discuss its correspondence to the gravitational case.
... Gravitational waves are disturbances in spacetime produced by the acceleration of masses, spreading outward as waves. 2,3 Detecting gravitational waves not only directly validates Einstein's predictions of general relativity, but also provides a unique method for observing and studying dense objects such as black holes. Significant progress was made in 2016 when the Laser Interferometer Gravitational-Wave Observatory (LIGO) reported the direct detection of gravitational waves. ...
Article
Predicting reliability is an essential part of the design phase for ensuring mission success. In the realm of gravitational wave detection, the integrity and dependability of the Grabbing, Positioning, and Release Mechanism (GPRM) are paramount for its effective space-based deployment. However, predicting reliability of a complex mechanical system like the GPRM during the design phase poses significant challenges due to the harsh and variable conditions of the space environment. This paper addresses these challenges by proposing a reliability evaluation method that combines the stochastic and degradation characteristics of the GPRM, according to which both randomness of the stud position and the degradation of the piezoelectric coefficient are considered. Failure criteria are established based on mission performance indicators, and the Kaplan-Meier estimator is used to analyze the mechanism reliability of the GPRM over time. The result predicts that the reliability of the GPRM is around 0.8 after 10 ⁷ operating cycles. This finding demonstrates that our proposed method is an effective approach for evaluating reliability, offering valuable insights for ensuring the long-term performance and successful operation of precision mechanisms.
... Fortunately, there already exist a number of introductory books on these topics. Particularly suitable for the material that is covered here is the approach of the textbooks by Weinberg (1972Weinberg ( , 2008, which can be used to find detailed explanations of some results quoted in this chapter concerning GR, cosmology and inflation. ...
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The aim of this chapter is to explain in clear and pedagogical terms how some particle-physics models and/or mechanisms can naturally lead to inflation and how this can provide testable predictions that can help us find new physics effects. Two well-established features of theoretical particle physics are linked to an essential property of inflation, a naturally-flat inflaton potential: (1) scale invariance, broken by small quantum corrections, and (2) Goldstone's theorem. It is also illustrated how to combine several scenarios of this type to obtain a rather general particle-physics motivated inflationary setup.
... However, inflation fails to provide an explanation for the time preceding the origin of the universe. As a result, the universe transitioned into the radiation era and, as the temperature decreased less than 10 3 K, the matter era advanced [5]. Currently, the universe undergoes accelerated expansion [6], attributed to either the cosmological constant or a form of dark energy with negative pressure violating the strong energy condition [7]. ...
Article
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This study explores the Bianchi type-V cosmological model with in the frame work of general relativity, featuring a perfect fluid governed by the polytropic equation in Lyra's Geometry, expressed p = αρ + kρ n , as proposed at [1]. We considered the case representing phantom universe for(1 + α + kρ n−1) 0, k < 0 , where ρ increases with the radius a(t). The role of Lyra;s Geometry has been discussed/ The solution to Einsteins field equation have been derived, providing insights into the physical and cosmological attributes of this particular model.
... The total anomaly for the entire dodecahedral system is obtained by summing the anomalies for all 12 string qubits: [12] For the theory to remain consistent, the total anomaly must vanish: [13] ...
Research
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This paper presents the Dodecahedron Linear String Field Hypothesis (DLSFH) as an extension of String Theory, aiming to provide deeper insights into fundamental particle interactions, symmetries, and forces. The key innovation of DLSFH is the incorporation of dodecahedral symmetry, where 12 string qubits are arranged on the vertices and edges of a dodecahedron. This geometric structure enhances the stability and coherence of interactions between particles, offering new explanations for phenomena beyond the Standard Model.
... Even if it is very small, the minimum length may be relevant in modifying the structure of a primordial phase transition. For example, in the first three minutes of the creation of the universe [35][36][37] a cosmological phase transition is believed to have occurred, generating a global change of the primordial matter. Starting at the Planck time t P ∼ 10 −44 s, the young universe evolved and by the time it reached t ∼ 10 −38 s the grand unified group SU(3) ⊗ SU(2) ⊗ U(1) had undergone gauge symmetry breaking. ...
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In the present contribution, a preliminary analysis of the effects of the Generalized Uncertainty Principle (GUP) with a minimum length, in the context of compact stars, is performed. On basis of a deformed Poisson canonical algebra with a parametrized minimum length scale that induces deviations from conventional Quantum Mechanics, fundamental questions involving the consistence, evidences and proofs of this approach as a possible cure for unbounded energy divergence are outlined. The incorporation of GUP effects into semiclassical 2N-dimensional systems is made by means of a time-invariant distortion transformation applied to their non-deformed counterparts. Assuming the quantum hadrodynamics σ−ω approach as a toy-model, due to its simplicity and structured description of neutron stars, we perform a preliminary analysis of GUP effects with a minimum spacetime length on these compact objects. The corresponding results for the equation of state and the mass-radius relation for neutron stars are in tune with recent observations with a maximum mass around 2.5 M⊙ and radius close to 12 km. Our results also indicate the smallness of the noncommutative scale.
... A straightforward calculation yields a vacuum energy density of the Planck order ∝ l −4 P . This contribution would correspond to a massive effective cosmological constant Λ, approximately 10 120 times greater than the currently estimated value [23]. For discussions on the possible evolving nature of the present cosmological constant, see [24][25][26][27][28]. ...
Preprint
We propose a revised formulation of General Relativity for cosmological contexts, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has no direct phenomenological impact on the Universe's dynamics or on particle motion within the expanding cosmos. Assuming a state close to vacuum, here defined by the vanishing product of the Einstein coupling constant and the Universe's energy density, we perform a Taylor expansion of the theory. In this framework, the vacuum energy problem is addressed, and an additional constant pressure term, which induces a Chaplygin-like contribution to the dark energy equation of state, arises in the late-time dynamics. The correction to the late-time Hubble parameter is investigated by comparing theoretical predictions with the late Universe observational data. Our findings indicate that the current value of the vacuum energy is consistent with zero. Alternatively, the expansion used in our formulation would no longer be valid if the current state significantly deviates from the assumed near-vacuum condition. Implications of the modified Λ\LambdaCDM model with respect to the Hubble tension are also discussed.
... where V eff is the effective potential. For a photon coming from a distant source, taking a turn at r tp and escaping then to a faraway observer the deflection angle is given by [40] θ(r tp ) = 2 ∞ rtp e Φ(r) dr (r 2 − rb(r)) r 2 ...
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In the present work, we seek for static spherically symmetric solutions representing wormhole configurations in generalized Rastall gravity (GRG). In this theory, a varying coupling parameter could act as dark energy (DE) and thus, it can be considered as responsible for the current accelerated expansion of the universe. We consider an anisotropic energy momentum tensor (EMT) as the supporting source for wormhole structure and further assume that there exists a linear relation between radial and tangential pressures and energy density. We therefore obtain two classes of solutions to the field equations of GRG, including the solutions with zero and nonzero redshift functions. For these solutions we find that the matter distribution obeys the physical reasonability conditions, i.e., the flare-out and the weak (WEC) and null (NEC) energy conditions either at the throat and throughout the spacetime. The conditions on physical reasonability of the wormhole solutions put restrictions on model parameters. Hence, in the framework of GRG, asymptotically flat wormhole configurations can be built without the need of exotic matter. Gravitational lensing effects of the obtained solutions are also discussed and it is found that the throat of wormhole can effectively act as a photon sphere near which the light deflection angle takes arbitrarily large values.
... In the cosmological perturbation theory, synchronous gauge has been studied extensively, see for e.g. [35]. The underlying idea is to use the gauge freedom of the theory to set the temporal-temporal and temporal-spatial components of the metric perturbation δg tt , δg ti equal to zero. ...
Preprint
Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism. We show that various gauge invariant variables obtained in the conventional analysis of cosmological perturbation theory correspond to Dirac observables tied to a specific choice of geometrical clocks. As examples, we show that the Bardeen potentials and the Mukhanov-Sasaki variable emerge naturally in our analysis as observables when gauge fixing conditions are determined via clocks in the Hamiltonian framework. Similarly other gauge invariant variables for various gauges can be systematically obtained. We demonstrate this by analyzing five common gauge choices: longitudinal, spatially flat, uniform field, synchronous and comoving gauge. For all these, we apply the observable map in the context of the relational formalism and obtain the corresponding Dirac observables associated with these choices of clocks. At the linear order, our analysis generalizes the existing results in canonical cosmological perturbation theory twofold. On the one hand we can include also gauges that can only be analyzed in the context of the extended ADM-phase space and furthermore, we obtain a set of natural gauge invariant variables, namely the Dirac observables, for each considered choice of gauge conditions. Our analysis provides insights on which clocks should be used to extract the relevant natural physical observables both at the classical and quantum level. We also discuss how to generalize our analysis in a straightforward way to higher orders in the perturbation theory to understand gauge conditions and the construction of gauge invariant quantities beyond linear order.
... The flux reaching us from this distance is then given by (Weinberg, 1972): ...
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One of the unresolved questions currently in cosmology is that of the non-linear accelerated expansion of the universe. This has been attributed to the so called Dark Energy (DE). The accelerated expansion of the universe is deduced from measurements of Type Ia supernovae. Here we propose alternate models to account for the Type Ia supernovae measurements without invoking dark energy.
... Proof. Following [54,7], we establish this in four key steps: ...
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This work establishes a universal bound on entanglement dynamics that proves more fundamental than and implies the speed of light as a derived quantity. Building upon recent work in quantum circuit complexity theory, we demonstrate that the rate of entanglement entropy change in any physical system is bounded by |dS/dt| ≤ 2E/πℏ, where E represents the system's total energy. We use quantum information geometry and local quantum field theories to prove that this bound naturally gives rise to the speed of light through the relationship c = v E = ℏG/l P , where v E represents the maximum velocity of entanglement propagation. We rigorously ground our results with spectral theory and operator methods to define a self-adjoint entanglement rate operator on an appropriate Hilbert space, proving it satisfies all requirements for physical observables including gauge invariance and a consistent measurement theory. We propose explicit protocols for measuring entanglement speed in quantum circuits and high-energy systems, deriving precise error bounds and resource requirements. Our analysis demonstrates that relativistic causality emerges from quantum information constraints, suggesting a fundamental reformulation of physics based on entanglement dynamics.
... Dark energy and dark matter are mysterious to compose our universe together with various material particles [1,2], which can form the generic black holes in some circumstance. While dark matter are now widely thought to be some form of massive exotic particles, such as primordial black hole formed within the first several second of our universe [3], it seems that black holes have nothing to do with dark energy because dark energy is not affected by gravity, no matter what size the black hole is and no matter where the dark energy locates around the horizon of the black hole. ...
Preprint
The "lost" information of black hole through the Hawking radiation was discovered being stored in the correlation among the non-thermally radiated particles [Phys. Rev. Lett 85, 5042 (2000), Phys. Lett. B 675, 1 (2009)]. This correlation information, which has not yet been proved locally observable in principle, is named by dark information. In this paper, we systematically study the influences of dark energy on black hole radiation, especially on the dark information. Calculating the radiation spectrum in the existence of dark energy by the approach of canonical typicality, which is reconfirmed by the quantum tunneling method, we find that the dark energy will effectively lower the Hawking temperature, and thus makes the black hole has longer life time. It is also discovered that the non-thermal effect of the black hole radiation is enhanced by dark energy so that the dark information of the radiation is increased. Our observation shows that, besides the mechanical effect (e.g., gravitational lensing effect), the dark energy rises the the stored dark information, which could be probed by a non-local coincidence measurement similar to the coincidence counting of the Hanbury-Brown -Twiss experiment in quantum optics.
... The most convenient choice is associated with the harmonic coordinates x α = (x 0 , x i ), where x 0 = ct, and t is the coordinate time. The class of the harmonic coordinates is used by the International Astronomical Union for description of the relativistic coordinates systems and for the data reduction [6,22] as well as in relativistic geodesy [63,64] The harmonic coordinates are defined by imposing the de Donder gauge condition on the metric tensor [65,66], ...
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Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, VLBI, SLR, and GNSS have achieved an unprecedented level of accuracy in measuring coordinates of the reference points of the ITRF and the world height system. The main geodetic reference standard is a normal gravity field represented in the Newtonian gravity by the field of a Maclaurin ellipsoid. The present paper extends the concept of the normal gravity field to the realm of general relativity. We focus our attention on the calculation of the first post-Newtonian approximation of the normal field that is sufficient for applications. We show that in general relativity the level surface of the uniformly rotating fluid is no longer described by the Maclaurin ellipsoid but is an axisymmetric spheroid of the forth order. We parametrize the mass density distribution and derive the post-Newtonian normal gravity field of the rotating spheroid which is given in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce the post-Newtonian multipolar expansion of the metric tensor given in terms of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy. Finally, we derive the post-Newtonian generalization of the Somigliana formula for the gravity field on the reference ellipsoid.
... Modified gravity is one of the two direct approaches for reproducing the late time acceleration observed in the Universe [1][2][3]. Additionally, there are other consistency problems that must eventually be tackled in the general relativity (GR) approach to gravity [4,5]. The question then becomes what reformulation of gravity should be adopted, or whether we should take an extension of GR as our starting position. ...
Preprint
General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleprallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f(R) gravity, on taking a generalization, f(T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f(R) gravity in that they are second order. In the present work, f(T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f(T) lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f(T) lagrangian. Observationally, both the auxiliary scalar field or exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way as is done in f(T) gravity.
... Problems with infinite self energies and self forces aside, however, it should be noticed that in the formal limit f e (|x|) → −e(4π|x| 2 ) −1 δ(|x|), together with the assumption that w e < C, the Nodvik charge-current density (5.3) reduces to the familiar expression for the spinless point charge [26,31], ...
Preprint
A new, relativistically covariant, massive Lorentz Electrodynamics (LED) is presented in which the bare particle has a finite positive bare rest mass and moment of inertia. The particle's electromagnetic self-interaction renormalizes its mass and spin. Most crucially, the renormalized particle is a soliton: after any scattering process its rest mass and spin magnitude are dynamically restored to their pre-scattering values. This guarantees that ``an electron remains an electron,'' poetically speaking. A renormalization flow study of the limit of vanishing bare rest mass is conducted for this model. This limit yields a purely electromagnetic classical field theory with ultra-violet cutoff at about the electron's Compton wavelength! The renormalized limit model matches the empirical electron data as orderly as one can hope for at the level of Lorentz theory. In particular, no superluminal equatorial gyration speeds occur.
... This is a characteristic dispersion of massive relativistic particles [29], where E g plays the role of rest energy. Upon employing the relativistic definition of the effective mass as m y = 2 k dE/dk y −1 , we obtain an effective mass for both CB and VB in the armchair direction to be m y = E g /2v 2 y = 0.12m 0 , a value close to the experimentally obtained 0.08m 0 [19], which could not be explained previously based on the parabolic approximation. ...
Preprint
We study the effects of a vertical electric field on the electronic band structure and transport in multilayer phosphorene and its nanoribbons. In phosphorene, at a critical value of the vertical electric field (EcE_c), the band gap closes and the band structure undergoes a massive-to-massless Dirac fermion transition along the armchair direction. This transition is observable in quantum Hall measurements, as the power-law dependence of the Landau-level energy on the magnetic field B goes from (n+1/2)B\sim (n+1/2)B below EcE_c, to [(n+1/2)B]2/3\sim [(n+1/2)B]^{2/3} at EcE_c, to [(n+1/2)B]1/2\sim [(n+1/2)B]^{1/2} above EcE_c. In multilayer phosphorene nanoribbons (PNRs), the vertical electric field can be employed to manipulate the midgap energy bands that are associated with edge states, thereby giving rise to new device functionalities. We propose a dual-edge-gate PNR structure that works as a quantum switch.
... This follows from the general fact that the second covariant derivative of a Killing vector is given by a contraction of the same Killing vector with the Riemann tensor (see e.g. [26]). Moreover, (2.49) implies that ...
Preprint
We study maximally supersymmetric AdSD_D solutions of gauged supergravities in dimensions D4D \geq 4. We show that such solutions can only exist if the gauge group after spontaneous symmetry breaking is a product of two reductive groups HR×HmatH_R \times H_\mathrm{mat}, where HRH_R is uniquely determined by the dimension D and the number of supersymmetries N while HmatH_\mathrm{mat} is unconstrained. This resembles the structure of the global symmetry groups of the holographically dual SCFTs, where HRH_R is interpreted as the R-symmetry and HmatH_\mathrm{mat} as the flavor symmetry. Moreover, we discuss possible supersymmetry preserving continuous deformations, which correspond to the conformal manifolds of the dual SCFTs. Under the assumption that the scalar manifold of the supergravity is a symmetric space we derive general group theoretical conditions on these moduli. Using these results we determine the AdS solutions of all gauged supergravities with more than 16 real supercharges. We find that almost all of them do not have supersymmetry preserving deformations with the only exception being the maximal supergravity in five dimensions with a moduli space given by SU(1,1)/U(1). Furthermore, we determine the AdS solutions of four-dimensional N=3 supergravities and show that they similarly do not admit supersymmetric moduli.
... As stated above, the standard PPN analysis fails in the present scenario, which is clearly anisotropic. A discussion involving anisotropy of inertia and its effect in the width of resonance lines can be found in Ref. [20] and references therein (see also Ref. [21]). Presented as a test between Mach's principle and the equivalence principle, it relies on the hypothetical effect the proximity to the large mass of the galactic core could have on the proton's mass. ...
Preprint
We study the vacuum solutions of a gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking (LSB), radial/temporal LSB and axial/temporal LSB. The purely radial LSB result corresponds to new black hole solutions. When possible, Parametrized Post-Newtonian (PPN) parameters are computed and observational boundaries used to constrain the Lorentz symmetry breaking scale.
... In this Section we work in (3+1) dimensions and follow the conventions of Weinberg [7]. Starting from next Section, the metric will be euclidean. ...
Preprint
We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for functional integral formulations of euclidean quantum gravity, regularized to avoid conformal instability. It could be regarded as the analogue of the Wilson loop of gauge theories and allows in principle, through numerical lattice simulations or other approximation techniques, non perturbative evaluations of the potential or of the effective coupling constant.
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This presentation builds upon the conceptual framework introduced in the April Fools' paper, "Engineered Graviton Condensates in a Room-Temperature Superconductor for a Unified Quantum Fibonacci Field Theory." While the original paper was intended as satire, it presented several intriguing ideas, including the possibility of graviton condensation within superconductors, the interaction between gravitational and electromagnetic fields, and the role of Fibonacci-structured magnetic fields in stabilizing quantum coherence. Despite its humorous origins, the core themes of the paper align with legitimate research questions in discrete spacetime physics, quantum gravity, and superconductivity. - This presentation integrates newly established scientific models such as the dodecahedron linear string field hypothesis (DLSFH), Discrete Geometric Quantum Gravity (DGQG), Discrete Geometric Phase Space (DGPS), and Discrete Geometric Diffusion (DGD) to reframe these speculative ideas within a rigorous theoretical and experimental framework. Instead of treating graviton condensation as a fictional construct, the focus shifts to exploring whether localized metric distortions or "Nano Warp Bubbles," can emerge within discrete spacetime and be manipulated through superconducting quantum materials. - To move beyond speculation, this presentation outlines potential experimental tests that the scientific community can undertake. These include investigating gravito-electromagnetic interactions in superconductors, examining the effects of Fibonacci-sequenced magnetic fields on quantum coherence, and probing for anomalous energy diffusion patterns that could signal localized spacetime distortions. If such effects are observed, they could provide insight into the fundamental nature of spacetime and energy transport at the quantum level, potentially leading to new technologies in quantum computing, spacetime modulation, and propulsion. - This presentation aims to take the most promising elements of the original satirical work and provide a structured pathway for scientific investigation. By engaging the research community in these experiments, it may be possible to determine whether these speculative concepts hold merit and contribute to advancing the understanding of quantum gravity and discrete spacetime engineering.
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The physical theory of relativity opens up a new understanding of physics and cosmology. Since the beginning of human civilization, the discussion of cosmology has always been related to theological or divine aspects. The initial theory of cosmology is geocentric, that the earth is the center of the cosmos and the universe was created instantly by God. The classical understanding and interpretation of the Holy Scriptures of Abrahamic religions is considered to be in line with the geocentric theory. The heliocentric theory - the sun as the center of the cosmos - emerged in the 16th century, shifting the geocentric understanding. The heliocentric understanding makes the discussion of cosmology separated from theological concepts. There was a dichotomy between religion and science. The concept of creation re-emerged in the early 20th century after Einstein's theory of relativity became the foundation for understanding contemporary cosmology. This paper discusses the implications of the theory of relativity and the development of cosmology on the understanding of the Godhead or Contemporary Theology. The research paper uses qualitative research methods with a library research approach and the analysis developed uses descriptive analysis methods, with the concept of the integration of science and theology. The results of research on relativity that space and time are relative quantities, become the basis for understanding the theory of the development of the cosmos. In accordance with Hubble's law, the universe continues to grow and when traced backwards, the universe originated from the "Big Bang" about 13.8 billion years ago. Before the big bang, the volume of the universe = zero, meaning that space and time had not yet been created, there was "Nothingness". The implication of the theory of relativity for theology is the scientific concept of the universe from "Nothing" to "Existence" which is not from the text of the holy book, affirming the belief in the existence of the Creator, namely God.
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This article introduces the Quantum Matrix Hypothesis, a theoretical framework that postulates the existence of a nonlinear, universal information matrix as the foundational medium underpinning quantum mechanics and space-time. Unlike traditional quantum fields, which operate within the confines of space-time, the quantum matrix exists beyond these constraints, enabling dynamic information exchange across quantum systems and direct interaction with space-time curvature. By addressing unresolved challenges such as quantum entanglement, vacuum energy discrepancies, and the integration of quantum mechanics with general relativity, this hypothesis provides a unifying perspective on the fundamental structure of the universe. This hypothesis aims to ignite discussion and inspire exploration, blending theoretical insights with bold predictions that could reshape our understanding of physics, cosmology, and technology.
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This extended article presents a thermomechanical approach for calculating the stress tensor from the thermodynamic potential of inhomogeneous fluids and some applications to ionic fluids. The technique, based on the invariance of the fluid’s thermodynamic potential with respect to spatial transformations of translation and rotation, offers an alternative to the general covariant approach developed by two of the authors. We apply this technique to both pure mean-field theories of fluids in general and a theory that includes thermal fluctuations of the order parameter, using the example of ionic fluids. Additionally, we apply the thermomechanical approach to fluid models with vector order parameters, such as liquid dielectrics. For this case, we obtain a general expression for the stress tensor. Furthermore, we discuss specific issues related to the calculation of disjoining pressure in ionic fluids confined in nanoscale slit-like pores with metal or dielectric walls, using the Coulomb gas model. To test the robustness of the proposed approach, we reproduce a number of known results from the statistical theory of inhomogeneous fluids and obtain several new ones.
Preprint
Baryon Acoustic Oscillations (BAO) are frozen relics left over from the pre-decoupling universe. They are the standard rulers of choice for 21st century cosmology, providing distance estimates that are, for the first time, firmly rooted in well-understood, linear physics. This review synthesises current understanding regarding all aspects of BAO cosmology, from the theoretical and statistical to the observational, and includes a map of the future landscape of BAO surveys, both spectroscopic and photometric.
Preprint
A theory of fossil turbulence presented in the 11th Liege Colloquium on Marine turbulence is "revisited" in the 29th Liege Colloquium "Marine Turbulence Revisited". The Gibson (1980) theory applied universal similarity theories of turbulence and turbulent mixing to the vertical evolution of an isolated patch of turbulence in a stratified fluid as it is constrained and fossilized by buoyancy forces. Towed oceanic microstructure measurements of Schedvin (1979) confirmed the predicted universal constants. Universal constants, spectra, hydrodynamic phase diagrams (HPDs) and other predictions of the theory have been reconfirmed by a wide variety of field and laboratory observations. Fossil turbulence theory has many applications; for example, in marine biology, laboratory and field measurements suggest phytoplankton species with different swimming abilities adjust their growth strategies differently by pattern recognition of several days of turbulence-fossil-turbulence dissipation and persistence times above threshold values, signaling a developing surface layer sea change. In cosmology, self-gravitational structure masses are interpreted as fossils of primordial hydrodynamic states.
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