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The Particle Problem in General Relativity
... In recent years, several papers [11,8,7] have studied the fate of particles traversing an Einstein-Rosen bridge. 3 The Einstein-Rosen bridge was constructed in the seminal paper [3] from the Schwarzschild solution (1) by the change of variables r = α + u 2 , where the new radial coordinate u is allowed to take any real value. The resulting spacetime contains two copies of the exterior Schwarzschild region r > α glued together at the wormhole throat r = α. ...
... An alternative change of variables r = α + |η| was suggested in [6,7]. Contrary to the original construction in [3], the resulting spacetime satisfies the Einstein field equations everywhere including at the throat η = 0 because a lightlike brane is added at the throat (see [6,7] for details). Here we propose to combine their change of variables with the Eddington-Finkelstein change of variables (2). ...
... Throughout the paper we use the (+, −, −, −) sign convention for the signature of the metric. This was the choice of most of the pioneers of relativity theory, including Einstein himself (as in e.g.[3]), Schwarzschild[12,13], Weyl[14], Lemaître[9], Eddington[2] or Finkelstein[4]. ...
Eddington–Finkelstein metric is obtained from the Schwarzschild metric by a change of the time variable. It is well known that a test mass falling into a black hole does not reach the event horizon for any finite value of the Schwarzschild time variable [Formula: see text]. By contrast, we show that the event horizon is reached for a finite value of the Eddington–Finkelstein time variable [Formula: see text]. Then we study in Eddington–Finkelstein time the fate of a massive particle traversing an Einstein–Rosen bridge and obtain a different conclusion than recent proposals in the literature: we show that the particle reaches the wormhole throat for a finite value [Formula: see text] of the time marker [Formula: see text], and continues its trajectory across the throat for [Formula: see text]. Such a behavior does not make sense in Schwarzschild time since it would amount to continuing the trajectory of the particle “beyond the end of time.”
... In their study, they boldly proposed the following: EPR = ER. EPR refers to quantum entanglement (19), and ER is short for wormhole (20). This puzzling formula links microscopic and macroscopic phenomena, pointing out that the exotic matter that stabilizes the wormhole energy field is quantum entanglement. ...
... If a pixel particle meets a seed particle, the gray seed value f kl is replaced by the average gray value of the particles in the seed area, represented by f . Only when two particles satisfy the entanglement Equation (19) are the two particles entangled together. They are then considered to be within one cluster as a new seed particle. ...
... Step 3: In cases where pixel quantum particles meet a seed quantum particle, check whether any particle is within the neighborhood range of the seed particle using Equation (19). Then, group them. ...
Purpose:
Although classical techniques for image segmentation may work well for some images, they may perform poorly or not work at all for others. It often depends on the properties of the particular image segmentation task under study. The reliable segmentation of brain tumors in medical images represents a particularly challenging and essential task. For example, some brain tumors may exhibit complex so-called "bottle-neck" shapes which are essentially circles with long indistinct tapering tails, known as a "dual tail." Such challenging conditions may not be readily segmented, particularly in the extended tail region or around the so-called "bottle-neck" area. In those cases, existing image segmentation techniques often fail to work well.
Methods:
Existing research on image segmentation using wormhole and entangle theory is first analyzed. Next, a random positioning search method that uses a quantum-behaved particle swarm optimization (QPSO) approach is improved by using a hyperbolic wormhole path measure for seeding and linking particles. Finally, our novel quantum and wormhole-behaved particle swarm optimization (QWPSO) is proposed.
Results:
Experimental results show that our QWPSO algorithm can better cluster complex "dual tail" regions into groupings with greater adaptability than conventional QPSO. Experimental work also improves operational efficiency and segmentation accuracy compared with current competing reference methods.
Conclusion:
Our QWPSO method appears extremely promising for isolating smeared/indistinct regions of complex shape typical of medical image segmentation tasks. The technique is especially advantageous for segmentation in the so-called "bottle-neck" and "dual tail"-shaped regions appearing in brain tumor images.
... In recent years, several papers [11,8,7] have studied the fate of particles traversing an Einstein-Rosen bridge. 3 The Einstein-Rosen bridge was constructed in the seminal paper [3] from the Schwarzschild solution (1) by the change of variables r = α + u 2 , where the new radial coordinate u is allowed to take any real value. The resulting spacetime contains two copies of the exterior Schwarzschild region r > α glued together at the wormhole throat r = α. ...
... An alternative change of variables r = α + |η| was suggested in [6,7]. Contrary to the original construction in [3], the resulting spacetime satisfies the Einstein field equations everywhere including at the throat η = 0 because a lightlike brane is added at the throat (see [6,7] for details). Here we propose to combine their change of variables with the Eddington-Finkelstein change of variables (2). ...
... Throughout the paper we use the (+, −, −, −) sign convention for the signature of the metric. This was the choice of most of the pioneers of relativity theory, including Einstein himself (as in e.g.[3]), Schwarzschild[12,13], Weyl[14], Lemaître[9], Eddington[2] or Finkelstein[4]. ...
The Eddington-Finkelstein metric is obtained from the Schwarzschild metric by a change of the time variable. It is well known that a test mass falling into a black hole does not reach the event horizon for any finite value of the Schwarzschild time variable $t$. By contrast, we show that the event horizon is reached for a finite value of the Eddington-Finkelstein time variable $t'$. Then we study in Eddington-Finkelstein time the fate of a massive particle traversing an Einstein-Rosen bridge and obtain a different conclusion than recent proposals in the literature: we show that the particle reaches the wormhole throat for a finite value $t'_1$ of the time marker $t'$, and continues its trajectory across the throat for $t'>t'_1$. Such a behavior does not make sense in Schwarzschild time since it would amount to continuing the trajectory of the particle "beyond the end of time."
... However, for a sake of simplicity, we restrict the to the Gabor quantization based on the choice of probe functions ψ. In Section 7, motivated by the 1935 Einstein-Rosen paper [9] the Gabor quantization is applied to the most elementary (and singular!) metric field of general relativity, namely the uniformly accelerated reference system. ...
... In their illuminating 1935 article [9], Einstein and Rosen state that Every field, in our opinion, must therefore adhere to the fundamental principle that singularities of the field are to be excluded. ...
... The restriction x 1 = 0 is necessary since the Ricci tensor is indeterminate on the hyperplane x 1 = 0. In view of regularisation the authors of [9] propose to modify the metric (7.1) with the introduction of a small constant ς as ...
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space $\left(x,k\right)$ into Hilbertian operators. The $x=\left(x^{\mu}\right)$'s are space-time variables and the $k=\left(k^{\mu}\right)$'s are their conjugate wave vector-frequency variables. The procedure is first applied to the variables $\left(x,k\right)$ and produces canonically conjugate essentially self-adjoint operators. It is next applied to the metric field $g_{\mu\nu}(x)$ of general relativity and yields regularised semi-classical phase space portraits $\check{g}_{\mu\nu}(x)$. The latter give rise to modified tensor energy density. Examples are given with the uniformly accelerated reference system and the Schwarzschild metric. Interesting probabilistic aspects are discussed.
... As in Schwarzschild geometry, the r curvature coordinate generates a coordinate singularity at r = b > 0 in Eq. (21), but that has no penetrable horizon on account of Eq. (20). With our procedure, it is straightforward to find either time-like or null geodesic equations and orbits for Eq. ...
... With our procedure, it is straightforward to find either time-like or null geodesic equations and orbits for Eq. (21) and express them in terms of unique turning points. Remarkably, as is the case for the 'splittable space-time' reduction of Schwarzschild metric, 4,5 all those geodesics formally coincide with space-like geodesics on the 'a-temporal' MT wormhole, 18 having a positive-definite metric ...
We outline a general procedure to derive first-order differential equations obeyed by geodesic orbits over two-dimensional (2D) surfaces of revolution immersed or embedded in ordinary three-dimensional (3D) Euclidean space. We illustrate that procedure with an application to a wormhole model introduced by Morris and Thorne (MT), which provides a prototypical case of a `splittable space-time' geometry. We obtain analytic solutions for geodesic orbits expressed in terms of elliptic integrals and functions, which are qualitatively similar to, but even more fundamental than, those that we previously reported for Flamm's paraboloid of Schwarzschild geometry. Two kinds of geodesics correspondingly emerge. Regular geodesics have turning points larger than the `throat' radius. Thus, they remain confined to one half of the MT wormhole. Singular geodesics funnel through the throat and connect both halves of the MT wormhole, perhaps providing a possibility of `rapid inter-stellar travel.' We provide numerical illustrations of both kinds of geodesic orbits on the MT wormhole.
... The space-time geometry of wormholes are topologically non simply connected. The idea of wormhole was initiated by Flamm [3] immediatlely, after Einstein's formulation of gravity and subsequently by Einstein and Rosen [4] and Wheeler [5]. Infact the name wormhole was first coined by John Wheeler [5]- [6] in 1962 by reinterpreting the Einstein-Rosen bridge [4] as a connector between two distant places in spacetime having no mutual interaction. ...
... The idea of wormhole was initiated by Flamm [3] immediatlely, after Einstein's formulation of gravity and subsequently by Einstein and Rosen [4] and Wheeler [5]. Infact the name wormhole was first coined by John Wheeler [5]- [6] in 1962 by reinterpreting the Einstein-Rosen bridge [4] as a connector between two distant places in spacetime having no mutual interaction. The modern development of wormhole geometry was initiated by Morris and Thorne [7] by introducing the idea of traversability [8]- [10] which gives the possibility for a human being to travel unchanged through the tunnel of the wormhole in both directions in a finite time. ...
The paper deals with static traversable wormhole having shape function a polynomial of the radial coordinate of degree 2. Embedding of the wormholes in space-time is examined both analytically and graphically. Also both timelike and null geodesics are studied in this wormhole geometry.
... By changing the parameters in (1) to B>A, the simple spheroid geometry changes to that of the globotoroid (GT), Figure 1). Here the loxodrome solutions connecting the 2 poles now pierce the S pole and form a wormhole connecting the N pole, hence, the poles are connected in the similar fashion as described by the Einstein-Rosen bridge [3]. By establishing the GT geometry, the three distinct topologies emerge. ...
... In addition, the baryonic matter flocks to the core field, (i.e., the ring-torus with the wormhole), while sparsely populates the rest of the GT field structure. The globe is mostly occupied by the dark energy with some dark matter and its condensates that may show up in form of halos [3]. ...
It is proposed that our universe in reality is the multiverse composed of abstract objects called the globotoroids. Standalone these entities form the world of simplicity, and when intertwined the entangled states form the world of complexity. This organization vastly increases reality choices in the multiverse, where all reality possibilities result from dynamics of the two worlds coexisting under the auspices of dark energy and dark matter. The moment mass enters into this realm, it materializes only one of the reality options available at its entry, and reveals the reality we experience. Investigating how such reality outcome is formed, and what are its components, are the goals of this report.
... The theory of GR predicts the existence of them, but none have been found so far. [20,21,22] These wormholes might not only connect two different locations in the universe, but they may also connect two separate universes with each other. If the mouth of the wormhole moves in a specific manner, then the wormhole can allow for time travel. ...
... Without the negative mass-energy density all we have is a black hole singularity embedded in two different spacetimes. [21,22] Hawking realized that a negative energy density can be developed in the area of a singularity, if black hole evaporation via the Hawking radiation (the black hole can radiate and loss mass) takes place. The idea is that the apparent loss of information vis hawking radiation is actually recovered in an alternate world present in the interior of the black hole inaccessible to our world. ...
In this paper we talk about the formation mechanism of the stellar gravitational singularities. To begin with we talk about the formation and evolution of stars and understand the Hertzsprung Russell diagram that teaches us how to classify stars. With the help of the diagram, we categorize the stars based of their physical parameters such as color, temperature, and mass. We then talk about the death cycle of different mass stars and what comes after when their fuels have been exhausted. Stars below the Chandrashekhar limit form a white dwarf at the end of their lives, while stars above the limit form a neutron star of a singularity. Further to find which of the heavy mass stars forms a singularity we look at the Tolman-Oppenheimer-Volkoff limit that states stars with mass above the limit will form singularities. The types of singularities formed depend on the solution of the general theory of relativity given by Schwarzschild, Kerr, Kerr-Newman, and Reissner-Nordström. Each of the theory aspect of the four solutions has been described to give a better understanding of the structure of the singularity formed. The paper also explains theories such as Wormholes and time travel in brief to try and explain what can replace the singularity.
... Wormholes are spacetime models where two asymptotically flat ends are connected by a throat. Historically, the first wormhole that was found was the so-called Einstein-Rosen bridge [1] that occurs in the maximal analytical extension of the Schwarzschild metric. However, the Einstein-Rosen bridge is non-traversable, i.e. an observer cannot travel at subluminal velocity from one side of the throat to the other. ...
We consider a class of stationary and axisymmetric wormhole spacetimes that is closely related to, but not identical with, the class of Teo wormholes. We fix a point $p$ (observation event) and a timelike curve $\gamma$ (worldline of light source). We prove that, under very mild conditions on $\gamma$, for infinitely many positive integers $\kappa$ there is a past-pointing lightlike geodesic $\lambda_{\kappa}$ of Morse index $\kappa$ from $p$ to $\gamma$, hence an observer at $p$ sees infinitely many images of $\gamma$. We discuss the possible turning points of light rays from $p$ to $\gamma$ and their limit behaviour in terms of potentials that determine the sum of centrifugal and Coriolis forces of observers in circular motion for the case that the observers' velocity approaches the velocity of light. We exemplify the general results with two specific wormhole spacetimes.
... • ER = EPR: basically, an ER-bridge 5 is created [92] between two BHs through EPRlike correlations [93] and can possibly resolve the paradox [94]. The main idea is that through acting on the radiation, we can create a thermofield double state with a smooth horizon resulting in a BH interior looking like an ER-bridge constructed from these dof. ...
This thesis fits into the conceptual framework of black holes and the information paradox. More specifically, it entails the search for entanglement islands within the context of twodimensional Jackiw–Teitelboim gravity. The starting point is to acquire the knowledge to make inquiries within this area of study. As such, we begin by a precursory literature study to introduce tools as entanglement entropy, black hole physics, holographic entanglement entropy, and semiclassical Jackiw–Teitelboim gravity. Thereafter, we compute islands in our setup. Unlike in literature, we consider a model for an evaporating black hole originating from a classical energy pulse. We make no assumptions about a potential heat bath, gravitating or not, but we are able to relate our setup to a situation as if a heat bath were glued to the boundary of our spacetime. As the resulting systems are nonlinear in the parameters, we rely on numerical results to extract meaningful information. Prototypical calculations involve the entropy in which the cutoffs, necessary to regulate divergences, are effectively ‘ignored’. This approach is followed
first. However, these cutoffs can be related to the boundary coordinates and potentially
affect the location of possible islands. To take this into account, we define a renormalised
entropy which gives a more natural measure from the viewpoint we will present – a boundary observer who collects the outgoing radiation. In both cases we numerically obtain a Page curve; the observer collected all the outgoing radiation and can reconstruct the black hole interior by acting on it – there is no information loss. Intriguingly, we discover that the latter model can exist in two phases depending on the sole dimensionless parameter – a phase with and a phase without islands.
... Wormholes originally are solutions to the field equations of General Relativity that show unexpected connections between two quite separated regions of the spacetime [1][2][3][4], occurring even in D-dimensional spacetimes and with several topologies ( [5], and references therein). They do not satisfy the energy conditions of the General Relativity, being necessary some type of exotic matter as source, with some exceptions [6][7][8][9][10][11]. Thus, the Casimir effect, that generally involves a e-mail: geova@fisica.ufc.br ...
In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy density and tension, differently from what happens in a 4-D scenario, in which case it has been shown recently, by the direct computation of the exact shape and redshift functions of a wormhole solution, that this is possible. We show that in a 3-D spacetime the same is not true since the arising of at least an event horizon is inevitable. We do the analysis for massive and massless fermions, as well as for scalar fields, considering quasi-periodic boundary conditions and find that a possibility to circumvent such a restriction is to introduce, besides the 3-D Casimir energy density and tension, a cosmological constant, embedding the surface in a 4-D manifold and applying a perpendicular weak magnetic field. This causes an additional tension on it, which contributes to the formation of the wormhole. Finally, we discuss the possibility of producing the condensed matter analogous of this wormhole in a graphene sheet and analyze the electronic transport through it.
... The classic example of a non-traversable wormhole is the Einstein-Rosen bridge which can be obtained from a coordinate transformation of the Schwarzschild black hole [1], i.e. it is part of the structures in a maximally extended Kruskal-Szekeres manifold. It is no wonder then any observer who attempts to cross such a wormhole would be terminated at the Schwarzschild singularity. ...
We numerically construct a symmetric wormhole solution in pure Einstein gravity supported by a massive $3$-form field with a potential that contains a quartic self-interaction term. The wormhole spacetimes have only a single throat and they are everywhere regular and asymptotically flat. Furthermore, their mass and throat circumference increase almost linearly as the coefficient of the quartic self-interaction term $\Lambda$ increases. The amount of violation of the null energy condition (NEC) is proportional to the magnitude of $3$-form, thus the NEC is less violated as $\Lambda$ increases, since the magnitude of $3$-form decreases with $\Lambda$. In addition, we investigate the geodesics of particles moving around the wormhole. The unstable photon orbit is located at the throat. We also find that the wormhole can cast a shadow whose apparent size is smaller than that cast by the Schwarzschild black hole, but reduces to it when $\Lambda$ acquires a large value. The behavior of the innermost stable circular orbit around this wormhole is also discussed. The results of this paper hint toward the possibility that the 3-form wormholes could be potential black hole mimickers, as long as $\Lambda$ is sufficiently large, precisely when NEC is weakly violated.
... Wormholes have a long history in general relativity: within only a year of Einstein finalising his formulation of the field equations, Flamm published an article hinting of possible spacetime "shortcuts" [58]. From here, wormholes were then investigated as solutions to the Einstein equations by Weyl in the 1920s [163], Einstein and Rosen in the 1930s [51], and by Wheeler in the 1950s [164]. After this, though, the field lay relatively dormant for close to 30 yers until the wormhole 'renaissance' in the late 1980s with the seminal papers by Morris, Thorne, and Yurtsever [103,104]. ...
The central theme of this thesis is the study and analysis of black hole mimickers. The concept of a black hole mimicker is introduced, and various mimicker spacetime models are examined within the framework of classical general relativity. The mimickers examined fall into the classes of regular black holes and traversable wormholes under spherical symmetry. The regular black holes examined can be further categorised as static spacetimes, however the traversable wormhole is allowed to have a dynamic (non-static) throat. Astrophysical observables are calculated for a recently proposed regular black hole model containing an exponential suppression of the Misner-Sharp quasi-local mass. This same regular black hole model is then used to construct a wormhole via the ''cut- and-paste'' technique. The resulting wormhole is then analysed within the Darmois-Israel thin-shell formalism, and a linearised stability analysis of the (dynamic) wormhole throat is undertaken. Yet another regular black hole model spacetime is proposed, extending a previous work which attempted to construct a regular black hole through a quantum ''deformation'' of the Schwarzschild spacetime. The resulting spacetime is again analysed within the framework of classical general relativity. In addition to the study of black hole mimickers, I start with a brief overview of the theory of special relativity where a new and novel result is presented for the combination of relativistic velocities in general directions using quaternions. This is succeed by an introduction to concepts in differential geometry needed for the successive introduction to the theory of general relativity. A thorough discussion of the concept of spacetime singularities is then provided, before analysing the specific black hole mimickers discussed above.
... A wormhole is a kind of spatial geometry resembling a tunnel that connects two different regions of the same space-time, or two different space-times. Such geometries as solutions to the gravitational field equations were first mentioned in [1][2][3][4], but they were not traversable in the sense that a subluminal particle could not travel from one "end of the tunnel" to the other and return back. Probably the first exact traversable wormhole solutions were discussed in [5,6] (1973) in the Einstein-scalar theory in which the scalar is of phantom nature, that is, has a wrong sign of the kinetic term in the Lagrangian. ...
We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions $f(R)$, $F(R)$ and $\tau_0(R)$, where $R$ is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic ($f >0$), parabolic ($f=0$) and elliptic ($f < 0$) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus if such a dust cloud is placed between two empty (Reissner-Nordstr\"om or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.
... We have provided some physical local mechanisms, compatible with the matter wave theory by Einstein-de Broglie-Schrödinger, that are able to reproduce EPR-like correlations. This suggests that there is no longer any reason to think that quantum mechanics cannot be modified in the way envisioned by de Broglie, Einstein and Schrödinger [40,41,42,44,45]. Indeed it is unfortunate that today most bohmians have forgotten what even Bohm later recognized [46,47], that is to say the importance of finishing the double solution program by de Broglie, where particles are nothing but classical solutions of relativistic non-linear wave equations. ...
A theory may appear in which such conspiracies inevitably occur, and these conspiracies may then seem more digestible than the non-localities of other theories. When that theory is announced I will not refuse to listen, either on methodological or other grounds." (J.S. Bell)
Abstract: In this paper we want to bring back on track the unfulfilled Einstein-de Broglie-Schrödinger program, recently taken up by A.O. Barut and others[29, 38]. This program was born before matrix mechanics (devel-opped by Born, Heisenberg and Jordan) and it is currently believed to be impossible due to Bell's theorem, since it is a local model on space-time. I will show that it is possible to build a model in accordance with this program that is able to explain the correlations observed in Bell-type experiments through a natural combination of memory and detection loopholes.
... In contrast, when cards appeared with more advanced words in the deck associated with specific areas of Chemistry, Biology and Physics, they presented some difficulty, due to the fact that they did not know the subject, however, even in these situations, they used their imagination and made abstractions to draw something they didn't know, as can be seen in Physics, to designate a singularity of space-time in the context of General Relativity, whose frontier is topologically trivial and which non-trivially connects two distinct points of spacetime, see figure 5. They are also known as Schwarzschild wormholes or Einstein-Rosen bridges (Einstein & Rosen, 1935), being modeled after specific vacuum solutions of Einstein's field equations. ...
This article proposes and discusses qualitatively the use of a didactic board game in Science Education for high school students. The game contemplates in an interdisciplinary way the areas of Physics, Biology, Chemistry and Astronomy and is based on the development of the cognitive structure of the students through the act of drawing the concepts addressed in the classroom, also aiming at socialization through teamwork and the inclusion of students with hearing impairment. The game was created in a physics teacher education course and also aims to promote reflection on teaching practice and the search for attractive teaching methodologies for students.
... Originally, wormholes are the imaginary objects that are used for time travels or fastthan-light journeys in science fictions. However, it is shown that wormholes [1][2][3][4] as the special spacetime structures play more and more important role in understanding the physics of our universe. Recent examples include: the Maldacena and Susskind's proposal of "ER=EPR" conjecture [5], the traversable wormholes from the double trace coupling between the boundaries of AdS black hole [6], Hayden-Preskill protocol realization [7] or quantum teleportation towards traversable wormholes [8], replica wormholes used to derive the island rule for the entanglement entropy of Hawking radiation [9][10][11], and humanly traversable wormhole solutions in general relativity [12,13]. ...
We propose that the thermodynamics and the kinetics of the phase transition between wormhole and two black hole described by the two coupled SYK model can be investigated in terms of the stochastic dynamics on the underlying free energy landscape. We assume that the phase transition is a stochastic process under the thermal fluctuations. By quantifying the underlying free energy landscape, we study the phase diagram, the kinetic time and its fluctuations in details, which reveal the underlying thermodynamics and kinetics. It is shown that the first order phase transition between wormhole and two black hole described by two coupled SYK model is analogous to the Van der Waals phase transition. Therefore, the emergence of wormhole and two black hole phases, the phase transition and associated kinetics can be quantitatively addressed in our free energy landscape and kinetic framework through the dependence on the barrier height and the temperature.
... This is the only explanation I can offer." Since 1935, we know about the Einstein-Rosen bridge [16]. Our kind of wormhole is a bit different, because it is traversable and attached to our manikin, no other manikin (photon) is able to use it. ...
Here, I present a new model of quantum mechanics. The first part of the concept is that motion involves wormholes and only wormholes for any object. The second part is that space waves under a particle. If a model is correct, all pieces of the puzzle should fit with no exception. Therefore, I investigated many phenomena of quantum mechanics – such as Heisenberg’s uncertainty principle, the quantum tunnelling, quantum measurement, entanglement, the double-slit experiment, the delayed choice quantum eraser experiments and some more – from the aspect of the concept and found no contradiction. I show how we may measure the length of a particle’s wormhole. I also offer two other experiments, showing that we may send information faster than light avoiding the causality problem. The consequences of the concept offer a solution for the dark matter and the dark energy problem.
... The idea of this singularity has stimulated imaginative hypotheses such as the existence of tunnels ("wormholes") connecting the center of the black hole with other points in the universe: "... our astronaut ... may be able to avoid hitting the singularity and instead falling through a 'wormhole' and come out in another region of the universe" [Hawking 1998, p. 91]. The existence of these wormholes, also known as Einstein-Rosen bridges, was hinted in 1916 [Flamm 1916], a few months after Schwarzschild published his solution for the gravitational field within a black hole [Schwarzschild 1916], and was clearly proposed by Albert Einstein and Nathan Rosen about twenty years later [Einstein and Rosen 1935]. Some popular representations of these ideas, which are always based on the questionable idea that a mass causes a hollow in a flat space and in our case a cavity with an infinite depth, are shown in Fig. 29. ...
For the layman, modern physics is like an immense and magnificent cathedral that is impressive in its complex and sophisticated architecture, and amazing in size and richness of the workmanship.
Yet, in this apparently almost complete edifice, there is no answer to a long series of basic and crucial questions, while in any case these answers are indispensable and preliminary to any general theory.
It is essential to avoid the confusion between appropriate and clarifying answers and false tautological answers or formulas that actually say nothing about the questions posed.
In this book, the starting point is the interpretation given by Einstein’s general relativity to explain the gravitational force not as an action at a distance but as an effect intrinsic to the deformation of space caused by a “mass”. This interpretation is extended to the explanation of any attractive or repulsive force as an effect of flattening of dimensions with positive or negative curvature, one for each force.
It offers, without any forcing, an explanation for most of the unsolved questions of physics, of the nature of a mass, matter and antimatter, of the structure of an atom, of the origin of natural constants, of the quantization of phenomena, etc. It also offers a different interpretation of the nature of electrons and black holes.
Furthermore, the existence of antimatter in protons, but not in neutrons, is also predicted, a phenomenon that appears to be documented by recent works.
This book is not written by a physicist but it is also highlighted why a professional physicist would have to overcome serious or insurmountable difficulties to give innovative answers to the fundamental unsolved problems of physics using concepts unrelated to those currently accepted.
... The study of wormhole started long back in 1916 by [3] in analyzing the Schwarzschild solutions. In 1935, Einstein and Rosen [4] constructed wormhole type solutions considering an elementary article model as bridge connecting two identical sheets. This mathematical representation of space being connected by a wormhole type solution is known as "Einstein-Rosen bridge". ...
The present paper deals with some wormhole solutions which are obtained by taking two different shape functions along with zero tidal force. For obtaining wormhole solutions, anisotropic fluid and a equation of state $p_t=-\frac{a}{\rho}$ related by Chaplygin gas are considered where $\rho$ is the energy density, $p_t$ is tangential pressure and $a$ is positive constant. Energy conditions are examined for two different models, and it is found that a major energy conditions are satisfied in a region.
... Recently, Susskind and Maldacena proposed that at Planck scales QG fluctuations and the texture of spacetime are related to Einstein-Podolski-Rosen (EPR) entangled states [26,27] through the equivalence with Einstein-Rosen (ER) wormholes [28], also known as the ER=EPR conjecture [29][30][31][32]. Up to now, no clear effects were observed [33,34] indicating either that the energy fluctuations should occur at spatial scales much below those hypothesized by the sub-millimetric models or that one has to analyze more in deep the possible interactions between photons and gravitons [35,36]. ...
We propose a new thought experiment, based on present-day Quantum Information Technologies, to measure quantum gravitational effects through the Bose-Marletto-Vedral (BMV) effect by revealing the gravitational $t^3$ phase term, its expected relationships with low-energy quantum gravity phenomena and test the equivalence principle of general relativity. The technique here proposed promise to reveal gravitational field fluctuations from the analysis of the stochastic noise associated to an ideal output of a measurement process of a quantum system. To improve the sensitivity we propose to cumulate the effects of the gravitational field fluctuations in time on the outputs of a series of independent measurements acted on entangled states of particles, like in the building of a quantum cryptographic key, and extract from the associated time series the effect of the expected gravitational field fluctuations. In fact, an ideal quantum cryptographic key, built with the sharing of maximally entangled states of particles, is represented by a random sequence of uncorrelated symbols mathematically described by a perfect white noise, a stochastic process with zero mean and without correlation between its values taken at different times. Gravitational field perturbations, including quantum gravity fluctuations and gravitational waves, introduce additional phase terms that decohere the entangled pairs used to build the quantum cryptographic key, with the result of coloring the white noise. We find that this setup, built with massive mesoscopic particles, can potentially reveal the $t^3$ gravitational phase term and thus, the BMV effect.
... These are cosmological entities without any singularity or event horizon [6] which leads to the study of non-standard matter and the contribution of gravity in its formation. In 1935 Einstein and Rosen gave the concept of Einstein-Rosen bridge that was the extension of the static wormhole [7]. In GR and modified gravity theories the solution of field equations gives the geometry of the wormhole as a shortcut between distant Universes [8]. ...
The presence of exotic matter for the existence of the wormhole geometry has been an unavoidable problem in GR. In recent studies researchers have tried to deal with this issue using modified gravity theories where the WH geometry is explained by the extra curvature terms and NEC's are not violated signifying the standard matter in the WH geometry. In the present article we are trying to find the solutions of traversable wormholes with normal matter in the throat within the framework of symmetric teleparallel gravity $f(Q)$ where $Q$ is the non metricity scalar which defines the gravitational interaction. We will examine the wormhole geometries for three forms of function $f(Q)$. First is the linear form $f(Q)=\alpha Q$, second a non -linear form $f(Q)=\alpha Q^2 + \beta$ and third one a more general quadratic form $f(Q)=\alpha Q^2 + \beta Q + \gamma$ with $\alpha$, $\beta$ and $\gamma$ being the constants. For all the three cases the shape function is taken as $b(r) = {\frac{r_{0}\ln(r+1)}{\ln({r_0}+1)}}$ where $r_0$ is the throat radius. A special variable redshift function is considered for the discussion. All the energy conditions are then examined for the existence and the stability of the wormhole geometry.
... Exotic matter is a hypothetical type of matter that is needed to violate the null energy condition (NEC), and it is the fundamental ingredient for forming a traversable wormhole. With the assistance of the event horizon, in 1935, Einstein and Rosen [4] proposed wormhole solutions that are known as Lorentzian wormholes or Schwarzschild wormholes. Generally, classical matter satisfies the energy conditions, but the Casimir effect and the Hawking evaporation are some quantum fields that violate the energy conditions. ...
This article describes the study of wormhole solutions in f(Q)
gravity with noncommutative geometry. Here, we considered two different f(Q)
models—a linear model f(Q)=αQ
and an exponential model f(Q)=Q−α(1−e−Q)
, where Q is the non-metricity and α
is the model parameter. In addition, we discussed the existence of wormhole solutions with the help of the Gaussian and Lorentzian distributions of these linear and exponential models. We investigated the feasible solutions and graphically analyzed the different properties of these models by taking appropriate values for the parameter. Moreover, we used the Tolman–Oppenheimer–Volkov (TOV) equation to check the stability of the wormhole solutions that we obtained. Hence, we found that the wormhole solutions obtained with our models are physically capable and stable.
... They are solutions to the Einstein's field equation (EFE) of general relativity (GR), describing two asymptotically flat regions of space-time connected by a tube or 'bridge'. Einstein and Rosen in their seminal 1935 work [2] aimed at unifying electromagnetism and gravity, and were the first to interpret such a solution as two asymptotically flat regions of space-time connected by a tube or 'bridge'. However, their solution was geodesically incomplete, owing to the presence of a physical singularity. ...
Traversable wormhole solutions in general relativity (GR) require \emph{exotic} matter sources that violate the null energy condition. $f(R)$ gravity has been studied extensively as a viable alternative to GR, and traversable wormhole solutions in $f(R)$ gravity have been discussed extensively. In this study, we analyze the energy conditions for spherically symmetric traversable Morris-Thorne wormholes in a recently proposed viable $f(R)$ gravity model. We analyze wormhole space-times considering both constant and variable redshift functions, and demonstrate that traversable wormholes can be realized in this theory with minimal or no violations of the null energy condition with suitable choices of model and metric parameters.
... Nonetheless, one can study its geometry at some fixed value of t, i.e. as part of a slice of constant U /V ), which turns out to be quite interesting. We restrict ourselves to the original description of the bridge by Einstein & Rosen (1935) themselves, since apart from some use in science fiction the idea seems to be of historical value only. ...
This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.
... Wormholes connect two distant spacetime points creating 'short-cut's that allow 'apparently faster than light' travel between those two points [1][2][3][4][5]. Initially the idea was taken seriously by its inventors and proponents [6][7][8]. Soon it was realised that the Einstein-Rosen "wormhole" is not, contrary to expectations, a stable structure. The wormhole opens up and closes too quickly for even a photon to 'travel' through. ...
Ellis–Bronnikov (EB) wormholes require violation of null energy conditions at the ‘throat’. This problem was cured by a simple modification of the ‘shape function’, which introduces a new parameter $$m\ge 2$$ m ≥ 2 ( $$m=2$$ m = 2 corresponds to the EB model). This leads to a generalised (GEB) version. In this work, we consider a model where the GEB wormhole geometry is embedded in a five dimensional warped background. We studied the status of all the energy conditions in detail for both EB and GEB embedding. We present our results analytically (wherever possible) and graphically. Remarkably, the presence of decaying warp factor leads to satisfaction of weak energy conditions even for the EB geometry, while the status of all the other energy conditions are improved compared to the four dimensional scenario. Besides inventing a new way to avoid the presence of exotic matter, in order to form a wormhole passage, our work reveals yet another advantage of having a warped extra dimension.
... Flamm [1] first realized this hypothetical connection in 1916. After that, Einstein and Rosen [2] used his concept and constructed a bridge so-called Einstein-Rosen bridge. Later, in 1957, the term wormhole was introduced by Wheeler, and Misner [3]. ...
We consider symmetric teleparallel gravity (STEGR), in which gravitational Lagrangian is given by the arbitrary function of non-metricity scalar Q to study static and spherically symmetric charged traversable wormhole solutions with non-commutative background geometry. The matter source at the wormhole throat is acknowledged to be anisotropic, and the redshift function has a constant value (thus, our wormhole solution is non-tidal). We derived numerically suitable forms of wormhole shape functions in the linear f (Q) = αQ + β and non-linear f (Q) = Q + mQ n STEGR models directly from the modified Einstein Field Equations (EFE's). Besides, we probed these models via Null, Dominant, and Strong energy conditions w.r.t. free MOG parameters α, β, m, and n. We also used Tolman-Oppenheimer-Vokloff (TOV) equation to investigate the stability of WH anisotropic matter in considered MOG. Finally, we plot the effective equation of state.
... The 'singularity' at 2M can be removed by a suitable choice of the parameters. This was pointed out by Einstein and Rosen [3]. They defined a new variable, which differs from our R by the factor 8M . ...
Some features of the Schwarzschild and Kruskal metric are being discussed
under the assumption that the Schwarzschild model can be explained geometrically.
... In view of general theory relativity (GR), Einstein and Rosen predicted the existence of bridges connecting two distant regions in spacetime named as Einstein-Rosen bridges or wormholes (WHs) [1,2]. Thereafter, the pioneering work of Morris and Thorne [3] developed the topological connections between separated regions of spacetime, as solutions of Einstein's field equations in GR, leading to the formation of three-dimensional TWH geometries. ...
We study the stability of circular orbits in the background of a traversable wormhole (TWH) spacetime obtained as a solution of Einstein's field equations coupled conformally to a massless scalar field. The Lyapunov stability approach is employed to determine the stability of circular orbits (timelike and null) of non-spinning test particles around a TWH spacetime. In the case of timelike geodesics, the particle is confined to move in four different types of effective potentials depending on various values of the angular momentum L with both centrifugal and gravitational part. The effective potential for null geodesics consists of only a centrifugal part. Further, we characterize each fixed point according to its Lyapunov stability, and thus classify the circular orbits at the fixed point into stable center and unstable saddle points by depicting the corresponding phase-portraits.
... Wormholes are space-time configurations with topologically simple boundaries and non-trivial interiors [1], generally interpreted as tubes or bridges connecting two asymptotically flat regions of space-time. Wormholes can be obtained as exact solutions of the Einstein's field equations (EFEs) in General Relativity (GR) [2,3], and lead to interesting physical implications. The most widely discussed of these is the prospect of traversable Lorentzian wormholes. ...
Traversable wormhole solutions in general relativity (GR) require exotic matter sources that violate the null energy condition, and such exotic behavior may be avoided in $f(R)$ modified gravity. Moreover, the concept of non-commutative geometry as a gravitational source can be leveraged both in GR and modified gravity to realize non-trivial space-time configurations. In this study, we investigate a viable $f(R)$ gravity model and non-commutative geometry to analyze spherically symmetric traversable Morris-Thorne wormhole solutions. We analyze the different energy conditions, and demonstrate that wormholes satisfying the energy conditions can be realized in both frameworks.
... Since the discovery of gravitational waves from binary black holes [3], there has been a rising interest in questioning the feasibility of equivalent phenomena in classical waves. It is very difficult to envisage or construct black holes in classical laboratory frame models due to the stringent constraint on massive mass (i.e., spacetime distortion) with the interplay between spacetime and energy-momentum (matter) information in general relativity [4]. Alternatively, we pursue curved elastic continuum to reveal the distortion equivalent to refractive index with spatial curvature for the emergence of such a black hole. ...
We present a black hole effect by strategically leveraging a conformal mapping in elastic continuum with curved-space framework, which is less stringent compared to a Schwarzschild model transformed to isotropic refractive index profiles. In the conformal map approach, the 2D point singularity associated to the black hole effect is accomplished by physical plates with near-to-zero thickness. The analog gravity around the singularity results in highly confined energy and lagged timings within a branch cut of the conformal map. These effects are quantified both numerically and experimentally in reference to control trials in which the thickness is not modulated. The findings would deepen our understanding of the elastic analog in mimicking gravitational phenomena, as well as establish the elastic continuum framework for developing a generic design recipe in the presence of the index singularity. Geometric landscapes with elastically curved surfaces would be applicable in a variety of applications such as sensing, imaging, vibration isolation, and energy harvesting.
... We set n = 0 because we assumed when there is no spatial entanglement there is no cell connecting them together. This is similar to the ER=EPR approach studying the relation between the Einstein-Rosen (ER) wormholes [22] and Einstein-Podolsky-Rosen (EPR) entanglement [23] by requesting the locality and the equivalence principle [24]. We see that when m = 0, there is no bridge exist to connect the two fields operators together, therefore φ(x 1 )φ(x 2 ) conn. ...
In this paper, we discuss the relation between the geometry of spacetime in terms of the entanglement of N localized scalar particles in flat space and suggest that the spacetime interval can be represented using the new picture as discrete fundamental cells. In the context of string theory, this can show the third quantization in the sense of quantized string length. We consider a two-dimensional string with n Planck length quantas and obtain its partition function using the JT gravity path integral. Qualitatively, we show that this string can have possible transitions to lower states of length quantas and have additional states for propagation. This propagation can play a crucial role in solving the black hole information loss and investigating different aspects of quantum gravity.
... A traversable wormhole, joining two otherwise distinct universes through two mouths and a throat, is also a complete solution of the Einstein's equations. A wormhole is a concept with a history of its own that in a sense was initiated by Einstein in the celebrated Einstein-Rosen bridge [25]. The concept had further developments related to the quantization of the spacetime geometry [26], and it was essential to understand the maximal extension of the Schwarzschild spacetime, now seen as a white hole being converted to a black hole through a nontraversable wormhole connecting two separated asymptotically flat spacetimes [27], which in turn gave rise to the notion of multiply connected spacetimes [28]. ...
Bubble universes and traversable wormholes in general relativity can be realized as two sides of the same concept. To exemplify, we find, display, and study in a unified manner a Minkowski-Minkowski closed universe and a Minkowski-Minkowski traversable wormhole. By joining two 3-dimensional flat balls along a thin shell two-sphere of matter, i.e., a spherical domain wall, into a single spacetime one gets a Minkowski-Minkowski static closed universe, i.e., a bubble universe. By joining two 3-dimensional complements of flat balls along a thin shell two-sphere of matter, i.e., a spherical throat, into a single spacetime one gets a Minkowski-Minkowski static open universe which is a traversable wormhole. Thus, Minkowski-Minkowski bubble universes and wormholes can be seen as complementary. It is also striking that these two spacetimes have resemblances with two well-known static universes. The Minkowski-Minkowski static closed universe resembles the Einstein universe, a static closed spherical universe homogeneously filled with dust matter and with a cosmological constant. The Minkowski-Minkowski static open universe resembles the Friedmann static universe, a static open hyperbolic universe homogeneously filled with negative energy density dust and with a negative cosmological, a universe with two disjoint branes that can be considered a failed wormhole. In this light, the Einstein and Friedmann universes are also two sides of the same concept. A linear stability analysis for all these spacetimes is performed. The complementarity between bubble universes and traversable wormholes, that exists for these static spacetimes, can be can carried out for dynamical spacetimes, indicating that such a complementarity is general. The study suggests that bubble universes and traversable wormholes can be seen as coming out of the same concept, and thus, if ones exist the others should also exist.
... Since these two 'frames of reference' are governed by the same principle of statistical mechanics, for an uninformed observer they must be thermodynamically identical. However, when the observer can 'see' the thermal landscape, they can clearly distinguish the two states (and perceive the notion of emergent forces and fluxes) -a viewpoint which is analogous to Einstein's weak principle of equivalence in relativity [56,57]. ...
An approach that extends equilibrium thermodynamics principles to out-of-equilibrium systems is based on the local equilibrium hypothesis. However, the validity of the a priori assumption of local equilibrium has been questioned due to the lack of sufficient experimental evidence. In this paper, we present experimental results obtained from a pure thermodynamic study of the non-turbulent Rayleigh-B\'enard convection at steady-state to verify the validity of the local equilibrium hypothesis. A non-turbulent Rayleigh-B\'enard convection at steady-state is an excellent `model thermodynamic system' in which local measurements provide no insights about the spatial heterogeneity present in the macroscopic thermodynamic landscape. Indeed, the onset of convection leads to the emergence of spatially stable hot and cold domains. Our results indicate that these domains while break spatial symmetry macroscopically, preserves it locally that exhibit room temperature equilibrium-like statistics. Furthermore, the role of the emergent heat flux is investigated and a linear relationship is observed between the heat flux and the external driving force following the onset of thermal convection. Finally, theoretical and conceptual implications of these results are discussed which opens up new avenues in the study non-equilibrium steady-states, especially in complex, soft, and active-matter systems.
... This hypothetical structure, which arises from the solutions of Einstein field equations, is not allowed to form by ordinary matter in General Relativity as the violation of null energy condition is inevitable in Einstein's theory. Although the subject of wormholes was introduced as early as 1916 by Flamm [1] and then by Einstein and Rosen [2], this area of research has been stimulated by Morris and Thorne when they published their paper in wormhole physics which became later a classical reference in the field [3]. In their work, Morris and Thorne studied traversable wormhole in the framework of General Relativity where they came up with the conclusion that the matter threading a static traversable wormhole must always be exotic as the violation of the energy conditions is unavoidable. ...
In this work, we show that any viable f(R) gravity model with constant scalar curvature could be implemented to construct wormholes that are supported by ordinary matter. In particular, the constructed wormholes give rise to attractive geometries at least in specific regions, if the ratio between the Lagrangian density function f(R) and its derivative F=df(R)dR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F=\frac{df(R)}{dR}$$\end{document} satisfies certain constraints. In this context, we derive static, spherically symmetric and traversable wormhole solutions supported by anisotropic matter field where both the weak and the strong energy conditions could be satisfied. The obtained solutions are physically realistic as they respect the asymptotic flatness condition. The case of traceless energy-momentum tensor is further investigated where it is shown that if the Ricci scalar is constant, then the only admitted f(R) gravity model is the one involving a square Lagrangian, i.e f(R)=cR2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R)=cR^2$$\end{document}. For this model we derived the constraints that allow the corresponding wormhole to satisfy the energy conditions.
... Today, many studies are actively investigating wormholes in space-time. This is because it was recently found that the Einstein-Rosen (ER) bridge [17] gives some type of Einstein-Podolsky-Rosen (EPR) pair [18][19][20][21], which plays a very important role in the literature on the information paradox [22]. It would be also its reason that there are common features and behaviors between AdS 2 wormholes and the SYK models, from which currently we can perform various interesting studies [23][24][25][26]. ...
In this study, we consider a gas in the Morris–Thorne traversable wormhole space-time, and analyze the critical temperature of the Bose-Einstein condensate in the vicinity of its throat. Our results show that it is equal to zero. Then, from this result, we point out that a state analogous to the Josephson junction is always formed at any temperature in the vicinity of its throat. This is of interest as a gravitational phenomenology. Of course, there is the problem of the exotic matter, but we perform this work without treating it.
... The wormholes structure was first introduced by Flamm [1], but his solutions suffered some stability problems. Later, Einstein and Rosen studied a similar structure of the wormhole and introduced a concept called the Einstein-Rosen Bridge [2]. These hypothetical objects lead to different static and non-static in proportion to the constant or variable radius of the wormhole throat. ...
... We know that quantum mechanics allows for Einstein-Podolsky-Rosen (EPR) correlations [120], which basically stem from the underlying entanglement structure of the wavefunction describing the system. On the other hand, one can find solutions in general relativity that can connect far away points of spacetime via wormholes [121] which are called Einstein-Rosen bridges (ER) [122]. These two phenomena seem to challenge the notion of locality [120]. ...
In this review, we present the ongoing developments in bridging the gap between holography and experiments. To this end, we discuss information scrambling and models of quantum teleportation via Gao-Jafferis-Wall wormhole teleportation. We review the essential basics and summarize some of the recent works that have so far been obtained in quantum simulators towards a goal of realizing analogous models of holography in a lab.
A "Big Bang" creation event which begins as a subatomic singularity leads to the question: where did the singularity come from? As detailed here, the evidence indicates that this (observable) "universe" recycles itself by expanding outward and collapsing back into a singularity which explodes outward again. The cosmos, however, may be infinite, and consist of innumerable "universes" all of which eventually collapse into a singularity which then mushrooms outward giving rise to new universes (including our own) and thus explaining why our universe behaves and is organized contrary to Big Bang theory. These theories of cyclic, oscillating universes and of repeated episodes of expansion, contraction, and colliding universes, have failed to generate widespread support, and are based on the beliefs that: A) this universe is expanding-when, it may already be accelerating toward a collapse-and that B) a singularity explodes outward. Quantum physics and relativity, however, predict that a singularity-which has shrunk to smaller than a Planck Length (1.61619926 x 10-33 cm), will blow an imploding hole through the fabric of the space-time quantum continuum, forming an Einstein-Rosen bridge and creating a mirror universe on the other side. The mirror of a positive-matter universe, is an antimatter universe. If cycles of creation alternate from antimatter to matter, and if a collapsing/imploding antimatter universe gave birth to our own, there is no violation of the second law of thermodynamics, entropy ceases to be a limiting factor, and the conservation laws of energy and mass are maintained. As predicted by Einstein's theory of relativity, and when coupled with quantum physics, it appears we may be dwelling in a Mirror Universe which formed from the remnants of a collapsing antimatter universe which upon shrinking to a singularity smaller than a Planck length, blew a hole in the quantum continuum thereby leading to the creation of this universe on the other side. Further, our Mirror Universe is not be expanding, but already collapsing and accelerating to its doom. If so, this collapse may account for the clumping and formation of great galactic walls separated by vast voids, colliding galaxies, and phenomenon attributed to the purely hypothetical "dark energy" which may not exist at all.
In this paper, we examine the embedded wormhole solutions in the modified [Formula: see text] theory of gravity, where [Formula: see text] denotes the trace of the energy–momentum tensor and [Formula: see text] is the Ricci scalar. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. We explore the feasible solutions for the specific model of [Formula: see text] theory of gravity. Energy conditions have been explored using the approach mentioned above. Conclusively, we find that obtained wormhole solutions are acceptable, as the null energy condition is violated in the specific region.
We construct optical appearance and profiled spectral lines of Keplerian discs with inner edge at the innermost circular geodesic located on both sides of reflection-symmetric Simpson-Visser wormholes, in dependence on their parameter and inclination angle of distant observers. We demonstrate significant differences in appearance of the discs on the our side and the other side of the Simpson-Visser wormholes. Large part of the other-side disc is always in dark region of the image of the disc orbiting on the our side, enabling thus a simple distinguishing in observations. The profiled spectral lines generated by the disc on the other side (our side) demonstrate strong (weak) dependence on the spacetime parameter, and weak (strong) dependence on the inclination angle; they have also different shape, giving thus other clues to clearly distinguish in observations reflection-symmetric wormholes as alternatives to black holes.
Ellis-Bronnikov (EB) wormholes require violation of null energy conditions at the `throat'. This problem was cured by a simple modification of the `shape function', which introduces a new parameter $m\ge 2$ ($m=2$ corresponds to the EB model). This leads to a generalised (GEB) version. In this work, we consider a model where the GEB wormhole geometry is embedded in a five dimensional warped background. We studied the status of all the energy conditions in detail for both EB and GEB embedding. We present our results analytically (wherever possible) and graphically. Remarkably, the presence of decaying warp factor leads to satisfaction of weak energy conditions even for the EB geometry, while the status of all the other energy conditions are improved compared to the four dimensional scenario. Besides inventing a new way to avoid the presence of exotic matter, in order to form a wormhole passage, our work reveals yet another advantage of having a warped extra dimension.
Several traversable wormholes (T-WHs) of the Morris-Thorne type have been presented as exact solutions of Einstein-nonlinear electrodynamics gravity (GR-NLED), e.g. \cite{Arellano,Bronnikov2017, Bronnikov_Walia, Canate_Breton, Canate_Breton_Ortiz, Canate_Magos_Breton}. However, none of these solutions is support by a nonlinear electrodynamics model satisfying plausible conditions. In this work, the first traversable wormhole solution of Einstein-nonlinear electrodynamics gravity coupled to a self-interacting scalar field (GR-NLED-SF) and with nonlinear electrodynamics model such that in the limit of weak field becomes the Maxwell electrodynamics, is presented.
In this short review we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaitre-Tolman-Bondi solution. They connect two copies of a closed Friedmann world filled with dust, or two otherwise distant parts of the same Friedmann world. Third, these are wormholes obtained in six-dimensional GR, whose one entrance is located in "our" asymptotically flat world with very small extra dimensions while the other "end" belongs to a universe with large extra dimensions and therefore different physical properties. The possible observable features of such wormholes are briefly discussed.
We numerically construct a symmetric wormhole solution in pure Einstein gravity supported by a massive $3$-form field with a potential that contains a quartic self-interaction term. The wormhole spacetimes have only a single throat and they are everywhere regular and asymptotically flat. Furthermore, their mass and throat circumference increase almost linearly as the coefficient of the quartic self-interaction term $\Lambda$ increases. The amount of violation of the null energy condition (NEC) is proportional to the magnitude of $3$-form, thus the NEC is less violated as $\Lambda$ increases, since the magnitude of $3$-form decreases with $\Lambda$. In addition, we investigate the geodesics of particles moving around the wormhole. The unstable photon orbit is located at the throat. We also find that the wormhole can cast a shadow whose apparent size is smaller than that cast by the Schwarzschild black hole, but reduces to it when $\Lambda$ acquires a large value. The behavior of the innermost stable circular orbit around this wormhole is also discussed. The results of this paper hint toward the possibility that the 3-form wormholes could be potential black hole mimickers, as long as $\Lambda$ is sufficiently large, precisely when NEC is weakly violated.
The black hole information loss paradox has long been one of the most studied and fascinating aspects of black hole physics. In its latest incarnation, it takes the form of the firewall paradox. In this paper, we first give a conceptually oriented presentation of the paradox, based on the notion of causal structure. We then suggest a possible strategy for its resolutions and see that the core idea behind it is that there are connections that are non-local for semiclassical physics, which have to be taken into account when studying black holes. We see how to concretely implement this strategy in some physical models connected to the ER=EPR conjecture.
The black hole information loss paradox has long been one of the most studied and fascinating aspects of black hole physics. In its latest incarnation, it takes the form of the firewall paradox. In this paper, we first give a conceptually oriented presentation of the paradox, based on the notion of causal structure. We then suggest a possible strategy for its resolutions and see that the core idea behind it is that there are connections that are non- local for semiclassical physics which have nonetheless to be taken into account when studying black holes. We see how to concretely implement this strategy in some physical models connected to the ER=EPR conjecture.
We study the timelike geodesic congruences in the generalized Ellis-Bronnikov spacetime (4D-GEB) and in recently proposed 5D model where a 4D-GEB is embedded in a warped geometry (5D-WGEB) and conduct a comparative study. Analytical expressions of ESR variables (for 4D geometries) are found which reveal the role of the wormhole parameter. In more general 4D and 5D scenarios geodesic equation, geodesic deviation equation and Raychaudhury equations are solved numerically. The evolution of cross-sectional area of the congruences of timelike geodesics (orthogonal to the geodesic flow lines) projected on 2D-surfaces yield an interesting perspective and shows the effects of the wormhole parameter and growing/decaying warp factors. Presence of warping factor triggers rotation or accretion even in the absence of initial congruence rotation. Presence of rotation in the congruence is also found to be playing a crucial role which we discuss in detail.
Considering a energy density of the form $\rho=q\left({\frac{r}{r_0}}\right)^{-n}$( where $q$ is an arbitrary positive constant with dimension of energy density and $n>0$), a shape function is obtained by using field equations of braneworld gravity theory in this paper. Under isotropic scenario wormhole solutions are obtained considering six different redshift functions along with the obtained new shape function. For anisotropic case wormhole solutions are obtained under the consideration of five different shape functions along with the redshift function $\phi=\beta ln(\frac{r}{r_0})$, where $\beta$ is an arbitrary constant. In each case all the energy conditions are examined and it is found that for some cases all energy conditions are satisfied in the vicinity of the wormhole throat and for the rest cases all energy conditions are satisfied except strong energy condition.
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