International Journal of Modern Physics D

International Journal of Modern PhysicsĀ D

Published by World Scientific

Online ISSN: 1793-6594

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Print ISSN: 0218-2718

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(Color online) Hawking–Page transition as a liquid/solid transtion.Ā Left. The Gibbs free energy as a function of temperature for fixed pressure P=1āˆ•(96Ļ€) is shown for a Schwarzschild-AdS black hole. The upper branch (blue, dashed) corresponds to small black holes; these have negative specific heat and so are thermodynamically unstable. The lower branch (red, solid) of large black holes has positive specific heat and for T>THP is the global minimum of G, thus corresponding to the thermodynamically preferred state. The free energy of the radiation (orange, solid) is normalized to zero; we see for T<THP it is the thermodynamically preferred state. There is a discontinuity in the first derivative of the radiation/black hole Gibbs free energy at THP, characteristic of a first-order phase transition. Right. The phase diagram shows that at any given pressure P there is a high-entropy phase at large T (corresponding to a large black hole) and a low-entropy phase at small T (corresponding to radiation). The coexistence line is of infinite length and is reminiscent of a solid/liquid phase diagram.
Black Hole Van der Waals behaviour.Ā Left. Plots of the Gibbs free energy of a charged-AdS black hole for several different values of the pressure P, displayed for fixed Q=1. For sufficiently low pressures P<Pc, a characteristic swallowtail emerges, shown by the red lines. Right. The Pāˆ’T phase diagram illustrates first order phase transition behaviour from small to large black holes as the temperature increases for fixed pressure. The coexistence line is analogous to a liquid/gas phase transition, and terminates at a critical point where the phase transition is of second-order. All quantities are in Planckian units.
(Color online) P-vĀ Diagram. The graph is a plot of pressure as a function of specific volume at various temperatures, obtained fromĀ (29) for a fixed Q=1. Maxwell’s equal area law is qualitatively displayed: the upper red isotherm T<Tc intersects the black isobar such that the areas above and below the isobar are equal. The quantitatively correct area law holds in the Pāˆ’v diagram for both black holes and Van der Waals fluids. For volumes vs<v<vl both the SBH (liquid) and LBH (gas) states coexist.
(Color online) Reentrant phase transition in a D=6 singly spinning Kerr-AdS black hole.Ā Left. The diagram illustrates the behaviour of G when an RPT takes place, which is for the range P∈(0.0553,0.0579). The arrows on the curves indicate the direction of increasing r+. At any point T>T1, the stable thermodynamic state is an LBH. Decreasing the temperature from this point, at T=T1 there is a first-order LBH/SBH phase transition after which the SBH is the stable state. As T is further decreased, the system follows the red curve until T=T0, where there is a cusp at which the lower blue dashed curve and the red curve join. Here G has a discontinuity at its global minimum; for smaller T the system jumps to the uppermost vertical red curve and becomes an LBH again. This corresponds to a zeroth-order SBH/LBH phase transition. Right. The Pāˆ’T diagram corresponding to the left panel illustrates 3 possible phases in the range P∈(0.0553,0.0579): an LBH region, an SBH region, and a region where no black hole solutions exist. The LBH and SBH are separated by coexistence lines corresponding to first-order (black curve) and zeroth-order (red curve) phase transitions. The first-order coexistence line eventually terminates at a critical point (not displayed). The angular momentum J=1.
Triple point.Ā Left: Phase diagram for a charged Einstein–Gauss–Bonnet black hole in D=6 dimensions with Q=1.¹²⁰ The small (SBH), large (LBH) and intermediate (IBH) black holes are in thermodynamic equilibrium at the triple point. There are two critical points: one where LBH and IBH become indistinguishable; the other, at a higher pressure, where SBH becomes indistinguishable from the LBH/IBH phase. Right: Phase diagram for water. There is a single critical point at P=218 atmospheres and T=374∘C.

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Black hole chemistry: The first 15 years

May 2025

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Robert B. Mann
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Aims and scope


Gravitation, astrophysics and cosmology are exciting and rapidly advancing fields of research. This journal aims to accommodate and promote this expansion of information and ideas and it features research papers and reviews on theoretical, observational and experimental findings in these fields. Among the topics covered are general relativity, quantum gravity, gravitational experiments, quantum cosmology, observational cosmology, particle cosmology, large scale structure, high energy astrophysics, compact objects, cosmic particles and radiation.

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Analysis of Geometric, Scalar Field, and Thermodynamic Properties of Hayward-like AdS Black Holes with Phantom Global Monopoles
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June 2025

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The case for a low matter density in dynamical dark energy model from local probes
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June 2025

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In this paper, we investigate, through a Bayesian study, the ability of a local low matter density Ī©M, in discrepancy with the value usually inferred from the CMB angular power spectrum, to accommodate observations from local probes without being in tension with the local values of the Hubble constant H0 or the matter fluctuation σ8 parameters. For that, we combine multiple local probes, with the criteria that they either can constrain the matter density parameter independently from the CMB constraints, or can help in doing so after making their relevant observations more model independent by relaxing their relevant calibration parameters. We assume however, either a dynamical dark energy model, or the standard Ī›CDM model, when computing the corresponding theoretical observables. We also add the latest Baryonic Acoustic Oscillations (BAO) measurements from the DESI year one release to some of our MCMC runs. We found that, within Ī›CDM model, for different combinations of our probes, we can accommodate a low matter density along with the H0 and σ8 values usually obtained from local probes, providing we promote the sound drag rs component in BAO calculations to a free parameter, and that even if we combine with the Pantheon + Supernova sample, an addition that was found in previous work to mitigate our concordance. Assuming w0waCDM, we also found that relaxing rs allow us to accommodate Ī©M, H0 and σ8 within their local values, with still however a preference for w0wa values far from Ī›CDM. However, when including Pantheon+ Supernova sample, we found that the latter preference for high matter density pushes σ8 to values much smaller than the ones usually obtained from local probes, mitigating by then a low matter density solution to the two common tensions. We conclude therefore that a low matter density value helps in preserving the concordance within Ī›CDM model, even with recent BAO DESI measurements or extended to high redshift supernovae sample, while the dynamical dark energy model ultimately fails to solve all tensions at once within our low density matter hypothesis.


(Color online) The mass deficit for a k=1 collapse can be understood as a volume excess (red region) for the same surface area (red line) with respect to euclidean space (yellow region).
(Color online) The equivalent situation for k=āˆ’1 can be illustrated using the fact that geodesics shooting off from the pole diverge, instead of converging as in the k=1 case. Filling in the space between them in red (right picture) leaves a volume deficit (the regions in white) with respect to an euclidean space with the same boundary area (yellow region). This translates into a mass surplus.
Simplest example of an LTB solution where A′=0 at an isolated point, with A′ changing sign, without shell-crossing.
An expanding inner k=āˆ’1 Universe which has outgrown the cavity size in the outer k=0 Universe. A large internal volume could therefore be hidden in side this structure.
Attractive voids

In this paper, we explore the well-known mass deficit/surplus phenomenon in General Relativity to suggest that it could play a part in the dark matter conundrum. Specifically in collapses and condensations of matter associated with negative intrinsic curvature of the foliation associated with the asymptotic boundary conditions, the external (ADM) mass can vastly exceed the integrated local energy over the internal volume. This can be phrased in terms of a deficit of volume for a given surface area (with respect to zero curvature). We explore the phenomenon in the context of generalizations of the Oppenheimer–Snyder models and other ā€œcut and pasteā€ models, the Lemaitre–Bondi–Tolman metric and several others. We produce constructions where the internal object is contracting or expanding, has a life time different from the asymptotic Universe, as well as a volume different than the excavated volume from the Universe. These are purely relativistic constructions and they could play a role in the puzzle of dark matter: attraction without visible or indeed any matter.


Semiclassical picture of gravitational collapse, in Eddington–Finkelstein coordinates. A shell collapses to a point, generating a singularity. Spacelike slices in this geometry stretch more and more as time evolves; this stretching leads to the creation of entangled pairs and the resulting information paradox.
(a) Small deformations of compact directions give scalar fields. (b) Larger deformations create planck scale solitonic objects like Kaluza–Klein monopoles. (c) Black hole microstates are ā€˜fuzzballs’: complicated bound sets of such nonperturbative objects.
A 1-dimensional illustration: (a) Neighboring pairs of spins entangle to a state which is largely a singlet, with a small admixture of the triplet. The triplets from two such pairs entangle to a singlet, giving a hierarchy of correlations between different length scales. (b) Expansion of space creates new pairs of spins in between, which must entangle with the previously existing spins in an appropriate way to yield the zero energy vacuum.
The fate of the collapsing shell, with our new picture of the gravitational vacuum. Entanglements between planck scale fluctuations are unable to relax to their vacuum values for scales of order the horizon radius. This leads to the creation of on-shell nonperturbative objects (black dots) on the evolving slice, which then link up to create fuzzballs (upper slice) of the kind in Fig.Ā 2(c).
Space cannot stretch too fast

In this paper, we argue that black holes microstates leave an imprint on the gravitational vacuum through their virtual fluctuations. This imprint yields a power law fall off — rather than an exponential fall off — for the entanglement of planck scale fluctuations at different points. These entanglements generate an extra energy when space stretches too fast, since causality prevents a relaxation of these entanglements to their vacuum values. We obtain semiclassical dynamics for slow processes like star formation, but a radical departure from semiclassicality when a black hole horizon forms even though curvatures remain low everywhere. This resolution of the information puzzle also implies an extra energy source at the scale of the cosmological horizon, which may explain the mysteries of dark energy and the Hubble tension.


The Universe according to DESI results

The recent fit of cosmological parameters by the Dark Energy Spectroscopic Instrument (DESI) collaboration will have a significant impact on our understanding of the universe. Given its importance, we conduct several consistency checks and draw conclusions from the fit. Specifically, we focus on the following key issues relevant to cosmology: (i) the acceleration of the universe’s expansion, which, according to the fit, differs over cosmological time compared to the standard cosmological model; (ii) the age of the universe, which appears slightly shorter than the age of the oldest stars; and (iii) the solution of the scale factor, both numerically and in an approximate analytical form.


A schematic diagram to show the main mechanisms for the formation of sBBHs, and the characteristics of the sBBHs formed from different astrophysical mechanisms.
(Color online) Multiband spectra of the GW events detected by LIGO and Virgo. The GW events shown here are from Abbott et al.²⁰¹ and each brown curve represents one event. The inspiralling phase of these kind of events may be detected by space-borne GW detectors, such as AMIGO, DECIGO, LISA, Taiji and Tianqin in the decihertz and millihertz bands. The sensitivity curves of LIGO, ET, CE, AMIGO, DECIGO, LISA, Taiji and Tianqin are also shown here, respectively, for illustration.
(Color online) Mass distribution of the primary components of those sBBH GW events detected by LIGO/Virgo in GWTC-3.²⁰¹ The black histogram shows the distribution of the detected sample by using the median mass of each primary component, and the magenta curve shows the distribution by considering the uncertainties in the mass estimate of each component. The green, red, blue and cyan curves show the merger rate density distribution obtained by the different models (Binned Gaussian process (BP), Flexible Mixtures (FM), Power-law+Spline (PS); and Power-law+Peak (PP), respectively) in Abbott etĀ al.²⁰¹ As seen at the high-mass end, there are at least two events with primary components’ mass in the upper-mass gap.
(Color online) Effective spin distribution of the sBBH GW events detected by LIGO/Virgo in GWTC-3.²⁰¹ The black histogram shows the distribution of the sample by using the median spin of each event. The red curves show the inferred effective spin distribution shown in Fig. 16 in Abbott et al.²⁰¹ The blue and green curves show the effective spin distributions by assuming that all BHs have initial spin value of 0.3 or 0.9 with randomly distributed relative spin directions.
(Color online) Total mass distributions of the Galactic BNSs and the GW detected BNSs. The black line shows the probability distribution of the total mass of GW170817, and the brown and magenta lines show the probability distribution of the total mass of GW190425, assuming low spin and high spin, respectively. Blue and red histograms show the total mass distributions obtained from the population synthesis model by adopting the DD2 equation of state for NSs in Chu et al.,²⁵² respectively. The green histogram shows the total mass distribution of those observed Galactic BNSs.
Compact binary coalescences: Formation, evolution, gravitational wave detection, and applications

Ground-based gravitational wave (GW) detectors primarily target several types of astrophysical sources. These include coalescence of compact binaries, such as stellar binary black holes, binary neutron stars, and neutron star-black hole binaries, as well as the stochastic GW background from numerous unresolved inspiralling and merging compact binaries across the universe. Other potential sources, such as core-collapse supernovae and rapidly rotating, nonspherical pulsars, are also anticipated, although their GW signals remain undetected. To date, the Laser Interferometer Gravitational wave Observatory (LIGO), Virgo and KAGRA (LVK collaboration) have successfully identified over 200 compact binary mergers. The GW signals from these mergers enable precise measurements of various system parameters, including distances, component masses, total masses, and spin magnitudes. Population studies of these mergers offer valuable insights into their formation mechanisms and evolution pathways. They also provide stringent constraints on fundamental physics such as neutron star equation of state and physical processes such as common envelope evolution that occur during their formation. Mergers involving neutron components can produce short Gamma-Ray burst and/or kilonova phenomena that can be observable through time-domain surveys and follow-up electromagnetic observations. When combined with the electromagnetic counterparts (if detected) and/or the information on host galaxies, these GW events can serve as bright or dark standard sirens to measure cosmological parameters with high precision. In this paper, we provide a brief review of the current status of compact binary coalescence studies and the detection of compact binary mergers by ground-based GW detectors. We focus on the formation and evolution of GW sources and discuss future prospects for development in this field.




Elementary considerations on possible entropy-driven cosmological evolutions

For several independent reasons, the idea that notorious sources of entropy could exist in the Universe has been recently revived. By taking advantage of a new framework accounting for nonequilibrium processes in cosmology, we explicitly investigate the cosmological dynamics as a function of the entropy production, focusing on the stability of the system. An exhaustive investigation is performed. As the main physical conclusion, we show that for a wide class of entropy source terms, the fluid dynamics converges toward an effective cosmological constant. Constraints on the associated entropic force are also obtained.


The scalar field at the horizon as a function of the normalized mass Māˆ•Ī» for black holes within scalar–Gauss–Bonnet gravity with a coupling functionĀ (179) having β=6. The right figure is a magnification of the left one. All nontrivial branches start from a bifurcation point at the trivial branch and they span either to M=0 (the first nontrivial branch) or they are terminated at some nonzero M (all the other nontrivial branches). Credit Ref. [81].
The scalar charge as a function of the normalized mass Māˆ•Ī» for the same black hole solutions as in Fig.Ā 1. The right figure is a magnification of the left one. Credit Ref. [81].
No-hair theorems in general relativity and scalar–tensor theories

In this paper, we consider the status of the classification of the vacuum, stationary and asymptotically flat black holes in scalar–tensor gravity. Contrary to the similar problem in general relativity, the black hole classification in scalar–tensor theories is much more challenging due to the very complicated character of the field equations and the very complex mathematical structure of the scalar–tensor gravity as a whole. We review most of the known no-hair results, and where possible new ones, as well demonstrate some of the difficulties that appear in our attempts to classify the black holes within scalar–tensor gravity. The proofs of the theorems and the underlying mathematical techniques are given in sufficient detail. To make the review self-contained, we also present the vacuum black hole uniqueness theorems in general relativity and their proofs.




Recent developments in gravitational lensing in observational cosmology

It has been now widely recognized that gravitational lensing is an indispensable research method in various areas of astronomy. In our previous review, we gave a pedagogical introduction of the subject and some applications in cosmology by that time. Since then, progresses in observations as well as theories of gravitational lensing have been remarkable and various works have been conducted. In this review, we highlight some of these developments.


Impact of Chaplygin gas model on the characteristics of gravastar in f(Q,T) gravity

In this paper, we study the properties of the gravastar, which is supported by Chaplygin gas. It is well known that Gravastar is a very lucrative alternative for black holes that do not suffer from the pathology of singularity. We have used a Chaplygin gas for the interior and shell as it can take the form of dark energy and a stiff matter phase. We also discussed the associated scalar field from which the Chaplygin gas can be derived. We find gravastar solutions in the f(Q,T) framework. We have also given physical motivation to how the Chaplygin gas can form during the stars’ collapse from residue scalar fields. We have calculated and plotted all the relevant physical properties, like proper length, entropy, energy, etc., for such a gravastar. We have also used the Israel junction condition to find the potential across the thin shell with respect to various regular black holes like Bardeen, Hayward, and holonomy-corrected black holes. We have calculated the speed of sound and hence commented on the stability of the gravastar for all four cases. We have also calculated the deflection angle for all such exteriors and given phenomenological predictions of how this model can be tested via next-generation radio telescopes. Finally, we conclude this paper by pointing out the future scope of our research.


Diagrams that contribute to graviton (wavy lines) loop corrections to the exchange of a massless scalar (solid lines) between two massive scalars (dashed lines). Each diagram is associated with an index i that labels which class of contribution that diagram (and its permutations) makes to the gauge-dependent coefficients reported in Table 2. The left-hand diagram is i=0, the center diagram is i=1 and the right-hand diagram is i=2 (which has four permutations).
Diagrams that contribute to graviton (wavy lines) loop corrections to the exchange of a massless scalar (solid lines) between two massive scalars (dashed lines). Each diagram is associated with an index i which labels which class of contribution that diagram (and its permutations) makes to the gauge-dependent coefficients reported in Table 2. The left-hand diagram is i=3 (two permutations), the center diagram is i=4 (four permutations) and the right-hand diagram is i=5 (four permutations).
Resummations for inflationary quantum gravity

May 2025

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5 Reads

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1 Citation

The continual production of gravitons during inflation endows loop corrections with secular logarithms which grow nonperturbatively large during a prolonged period of inflation. The physics behind these effects is reviewed, along with a catalog of the examples which have so far been found. Resummation can be accomplished by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. The issue of gauge independence is also addressed.


On possible scenario of relic wormhole formation

May 2025

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12 Reads

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1 Citation

It is known that in the presence of Euclidean wormholes the vacuum state is unstable, which, in general, leads to a number of phase transitions in the early Universe. According to the Kibble scenario during the phase transitions, defects of the domain-wall-type were formed. The specific feature of Euclidean wormholes is that a part of defects possesses negative energy and violates the energy conditions. The macroscopic character of such defects allows already the formation of a stable Lorentzian wormhole. This gives reason to consider relic wormholes as realistic astrophysical objects.



Acoustic black hole in noncommutative space: Solutions and thermodynamical analysis

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The inability of sound disturbances to escape from a fluid moving faster than sound is known as an acoustic black hole. These black holes either create or encourage this radiation, which is called phono-Hawking. On the other hand, the event horizon is a sound black hole’s boundary. Our goal is to use the spatial–spatial quatification provided by inspired noncommutativity to observe the quantum influence on sonor black hole features. The stuff characterizing the fluid is affected by such a distortion.


On the Unruh effect and the thermofield double state

May 2025

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1 Read

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1 Citation

The purpose of this review is to provide a pedagogical development of the Unruh effect and the thermofield double state. In Sec. 2, we construct Rindler spacetime and analyze the perspective of an observer undergoing constant acceleration in Minkowski spacetime, which motivates the establishment of the relationship between the Fourier modes in both geometries using the Bogoliubov–Valatin transformation. In Sec. 3, we explore the underlying physics leading to the Unruh effect, its analogy with the thermal radiation observed around a Schwarzschild black hole, and its manifestation through the coupling of a particle detector to the scalar field. Finally, in Sec. 4, we derive the thermofield double state by conducting a Euclidean analysis of the field and geometry.


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