Black Hole Entropy Research Articles

Thermodynamics of stealth black holes

Using Euclidean methods we investigate the thermodynamics of stealth black hole solutions, which are solutions that geometrically are indistinguishable from those of general relativity; however, they are accompanied by a nontrivial additional field that does not backreact to the metric. We find that in general, one can observe shifts in the mass and/or the entropy of such black holes; hence, at least at the thermodynamic level, the stealth solutions may be distinguished by those of general relativity. We also point out an example, the , where a nontrivial scalar field can accompany an (A)dS-Schwarzschild black hole without altering the thermodynamic quantities. We point out that thermodynamic discrepancies arise due to the additional boundary terms emanating from the stealth fields, where care should be given in order for the theory at hand to possess a well-defined variational procedure. Published by the American Physical Society 2025

Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein–Maxwell-charged scalar field system in spherical symmetry which are exactly isometric to extremal Reissner–Nordström after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. In particular, our result can be viewed as a definitive disproof of the “third law of black hole thermodynamics.” The main step in the construction is a novel C^{k} characteristic gluing procedure, which interpolates between a light cone in Minkowski space and a Reissner–Nordström event horizon with specified charge to mass ratio \frac{e}{M} . Our setup is inspired by the recent work of Aretakis–Czimek–Rodnianski on perturbative characteristic gluing for the Einstein vacuum equations. However, our construction is fundamentally nonperturbative and is based on a finite collection of scalar field pulses which are modulated by the Borsuk–Ulam theorem.

Phase structure and optical properties of the de Sitter Spacetime with KR field based on the Lyapunov exponent

Since the spontaneously broken of the Lorentz symmetry in the gravity theory with the non-minimally coupling between the Kalb–Ramond (KR) field (that acquires a nonzero vacuum expectation value) and the Einstein gravity, there exists the exactly static and spherically symmetric black holes solutions related with the Lorentz violating parameter. Based on this, we consider the corresponding black hole solution in the de-Sitter (dS) spacetime with the KR field and investigate the thermodynamic properties in the expanded phase space through introducing the interplay entropy between the black hole and cosmological horizons. Especially we analyze the effect of the Lorentz-violating parameter on the thermodynamic properties. Furthermore, the Lyapunov exponent and the shadow of these static and spherically symmetric black holes in this Lorentz-violating gravity theory are also investigated. These study will open a new perspective to probe the thermodynamics of black holes.

Nonextensive black hole thermodynamics from generalized Euclidean path integral and Wick’s rotation

This paper extends the Euclidean path integral formalism to account for nonextensive thermodynamics. Concretely, we introduce a generalized Wick’s rotation from real time t to imaginary time τ such that, t→-ifα(τ), where fα a differentiable function and α is a parameter related to nonextensivity. The standard extensive formalism is recovered in the limit α→0 and f0(τ)=τ. Furthermore, we apply this generalized Euclidean path integral to black hole thermodynamics and derive the generalized Wick’s rotations given the nonextensive statistics. The proposed formulation enables the treatment of nonextensive statistics on the same footing as extensive Boltzmann–Gibbs statistics. Moreover, we define a universal measure, η, for the nonextensivity character of statistics. Lastly, based on the present formalism, we strengthen the equivalence between the AdS-Schwarzschild black hole in Boltzmann–Gibbs statistics and the flat-Schwarzschild black hole within Rényi statistics and suggest a potential reformulation of the AdS5/CFT4 duality.

The information conservation in Hawking radiation by laws of thermodynamics

By solving the field equation in curved spacetime, we obtained the relative emissivity of the Kerr–Newman black hole. The results show that the relative emissivity satisfies the Boltzmann distribution law. With the first law of thermodynamics, we found that the emissivity is related to the entropy change of black holes which helps us solve the information loss in the Hawking radiation. Through calculating the information entropy of black holes, it is shown that the information conservation is satisfied in the Hawking radiation. Furthermore, we also studied the contribution of space-time background to Hawking radiation.

Islands for black holes in a hybrid quantum state

Following our previous work on hybrid quantum states in the Russo-Susskind-Thorlacius model, we study its most interesting solution representing a completely regular spacetime with the structure of causal diamond, containing an apparent horizon and radiation at infinity. Adapting recent computations of radiation entropy in terms of the entropy of entanglement, we find that this entropy follows a Page curve. This confirms our previous result [], which was obtained by directly calculating the thermodynamic entropy of radiation at infinity. We also investigate the presence of a possible island in these systems and find that it does not seem to play a role in contributing to the generalized black hole entropy. Published by the American Physical Society 2025

Phantom hairy black holes and wormholes in Einstein-bumblebee gravity

In this paper we study Einstein-bumblebee gravity theory minimally coupled with external matter – a phantom/non-phantom (conventional) scalar field, and derive a series of hairy solutions – bumblebee-phantom (BP) and BP-dS/AdS black hole solutions, regular Ellis-bumblebee-phantom (EBP) and BP-AdS wormholes, etc. We first find that the Lorentz violation (LV) effect can change the so-called black hole no-hair theorem and these scalar fields can give a hair to a black hole. If LV coupling constant ℓ>-1-1$$\\end{document}]]>, the phantom field is admissible and the conventional scalar field is forbidden; if ℓ<-1, the phantom field is forbidden and the conventional scalar field is admissible. By defining the Killing potential ωab, we study the Smarr formula and the first law for the BP black hole, find that the appearance of LV can improve the structure of these phantom hairy black holes – the conventional Smarr formula and the first law of black hole thermodynamics still hold; but for no LV case, i.e., the regular phantom black hole reported in (Phys Rev Lett 96:251101), the first law cannot be constructed at all. We also show there still exists a stable circular orbit around the BP black hole. When the bumblebee potential is linear, we find that the phantom potential and the Lagrange-multiplier λ behave as a cosmological constant Λ.

Tantum gravity

We argue there is an interesting triple-scaling limit of quantum gravity, namely when Planck’s constant scales to infinity while Newton’s constant and the speed of light tend to zero, keeping fixed the gravitational coupling GNc−4 and the combination ℏc. We refer to this limiting theory as “tantum gravity” and describe in this Letter some of its main properties and prospects for physics. Most notably, the laws of black hole thermodynamics survive this limit, which means that puzzles related to black holes and their evaporation could be addressed more easily in tantum gravity than in fully fledged quantum gravity. Published by the American Physical Society 2025

Thermodynamic aspects of higher-dimensional black holes in Einstein–Gauss–Bonnet gravity through exponential entropy

Abstract We assume exponential corrections to the entropy of $5D$ charged AdS&amp;#xD;black hole solutions, which are derived within the framework of&amp;#xD;Einstein Gauss-Bonnet gravity and nonlinear electrodynamics.&amp;#xD;Additionally, we consider two distinct versions of $5D$ charged AdS&amp;#xD;black holes by setting the parameters $q\rightarrow0$ and&amp;#xD;$k\rightarrow0$ (where $q$ represents charge, $k$ is the non-linear&amp;#xD;parameter). We investigate these black holes in the extended phase&amp;#xD;space, where the cosmological constant is interpreted as pressure,&amp;#xD;and demonstrate the first law of black hole thermodynamics. The&amp;#xD;focus extends to understanding the thermal stability or instability,&amp;#xD;as well as identifying first and second-order phase transitions.&amp;#xD;This exploration is carried out through the analysis of various&amp;#xD;thermodynamic quantities, including heat capacity at constant&amp;#xD;pressure, Gibbs free energy, Helmholtz free energy, and the trace of&amp;#xD;the Hessian matrix. In order to visualize phase transitions,&amp;#xD;identify critical points, analyzing stability and provide&amp;#xD;comprehensive analysis, we have made the contour plot of the&amp;#xD;mentioned thermodynamic quantities and observed that our results are&amp;#xD;very much consistent. These investigations are conducted within the&amp;#xD;context of exponentially corrected entropies, providing valuable&amp;#xD;insights into the intricate thermodynamic behavior of these $5D$&amp;#xD;charged AdS black holes under different parameter limits.

Thermodynamics of Black Holes with Rényi Entropy from Classical Gravity

Thermodynamics of Black Holes with Rényi Entropy from Classical Gravity

Evolution of interior entropy of a loop quantum-corrected black hole pierced by a cosmic string

Evolution of interior entropy of a loop quantum-corrected black hole pierced by a cosmic string

Third law of black hole mechanics for supersymmetric black holes and a quasilocal mass-charge inequality

It has recently been proved that a third law of black hole mechanics does not hold for Einstein-Maxwell theory coupled to a massless charged scalar field: there exist solutions that describe gravitational collapse to form an exactly extremal Reissner-Nordström black hole in finite time. In this paper it is proved that such solutions do not exist in theories with matter fields satisfying a local mass-charge inequality. In such a theory, if a 2-surface has the same metric, extrinsic curvature, and Maxwell field as a cross section of an extremal Reissner-Nordström horizon then this surface cannot have a compact interior and so cannot be a horizon cross section of a black hole formed in gravitational collapse. This result is proved using spinorial techniques, which are also used to prove a mass-charge inequality for a modified version of the Dougan-Mason quasilocal mass. Published by the American Physical Society 2024

Reviving QFT in ( 2+1 )-dimensional de Sitter spacetime

We consider a conformally coupled scalar quantum field theory (QFT) on (2+1)-dimensional static Einstein universe R×S2 and write down the free theory Hilbert space. We explain that this theory is secretly a QFT in (2+1)-dimensional de Sitter space because all the quantum observables experience “quantum revivals,” which naturally restricts the timelike R to the appropriate de Sitter time range. Our construction circumvents the causal obstruction to formulating QFT in de Sitter due to event horizons. There are not any in static Einstein. The “unitary gauge” description of the theory is realized by the zonal harmonics Pℓ(n^·n^′). We verify that interactions with conformally invariant external sources are mediated only by these modes. Hence these modes comprise the complete basis of the “bulk” theory. When the theory is cut off in the UV, the basis dimension scales as the Bekenstein-Hawking formula. Published by the American Physical Society 2024

Thermodynamics of charged four-dimensional hairy black holes

Thermodynamics of charged four-dimensional hairy black holes

Schottky Anomaly of Reissner-Nordstr"{o}m-de Sitter spacetime

Abstract In the extended thermodynamics of black holes, there exists a thermodynamical pressure whose dual thermodynamical quantity is volume. Extensive studies have been conducted on the phase structure of numerous black holes, which have demonstrated striking similarities to the phase structure of various ordinary matter systems. From the comparison of the thermodynamic properties between spherically symmetric AdS black holes and ordinary thermodynamic systems we known that the isovolumetric heat capacity of the former is zero, whereas that of the latter is non-zero. It is a subject of interest for the intrinsic reason for this discrepancy. For the Reissner-N"{o}rdstrom-de Sitter (RN-dS) spacetime with the coexistence of the black hole and cosmological horizons the effective thermodynamic quantities as well as the interaction between two horizons are presented. The heat capacity in the Reissner-N"{o}rdstrom-de Sitter (RN-dS) spacetime is then investigated, and it is demonstrated that the behavior of the heat capacity in the RN-dS spacetime is analogous to that of Schottky specific heat. Treating two horizons in the RN-dS spacetime as two distinct energy levels in a two-energy-level system we investigate the thermodynamic properties in the RN-dS spacetime with the method of studying the thermodynamic properties in an ordinary two-energy system, thereby elucidating the intrinsic reasons for the occurrence of Schottky specific heat in the RN-dS spacetime. The heat capacity observed in the RN-dS spacetime is not only consistent with that of the Schottky specific heat described by the effective thermodynamic quantities in the RN-dS spacetime, but also with that of an ordinary two-energy-level system. These results not only reveal the quantum properties of the RN-dS spacetime, but also provide a new avenue for further in-depth study of the quantum properties of black holes and dS spacetime.

Mixed gauge-global symmetries, elliptic modes, and black hole thermodynamics in Hořava-Lifshitz gravity

In Hořava-Lifshitz gravity, a putative consistent theory of quantum gravity for which there is evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is “mixed”: it is a local symmetry in one coordinate yet global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. The mixed symmetry and associated charge has not yet been accounted for in calculations of universal horizon thermodynamics in Hořava-Lifshitz gravity. This has led to problems, in particular the failure of the first law in a class of asymptotically AdS solutions where the normal to the leaves of the foliation is not aligned with the time translation Killing vector at infinity. We show how the dynamics of the charge corresponding to this symmetry coupled with the other features above resolves this issue. We then briefly comment how this mixed symmetry, the corresponding charge, and the elliptic equations of motion also conspire to evade recent holographic arguments for only local gauge fields in consistent theories of quantum gravity due to the lack of splittability of the elliptic equation and associated mode.

Quantum tunneling of fermions from kerr-like black holes within topologically massive gravity

In the framework of 3-D general relativity, this study explores a Kerr-like black hole solution with a focus on its causal structure and particle dynamics, employing Penrose diagrams to elucidate the spacetime geometry. The research investigates the behavior pf particles in the vicinity of the event horizon, analyzing their trajectories and potential fates, including the influence of the black hole’s rotation and gravitational effects. The Dirac equation is solved in this curved spacetime using “WKB approximation”, allowing the computation of the Hawking temperature and unveiling quantum effects associated with black hole geometries in three dimensions. Moreover, the phenomenon of superradiance is explored, highlighting the mechanisms through with the rotational energy and angular momentum of the black hole are extracted. This phenomenon provides deeper insights into energy transfer processes and the stability of such black hole solutions. The research contributes to a better understanding of black hole thermodynamics, particularly in lower-dimensional gravitational settings, and offers a comprehensive analysis of energy exchange processes. By integrating classical and quantum perspectives, this study enhances the comprehension of particle dynamics, quantum field behavior, and thermodynamic properties of black holes, enriching the broader field of lower-dimensional gravitational models and their implications for fundamental physics.

Thermodynamics of Charged Acoustic Black Hole: Heat Engine

Thermodynamics of Charged Acoustic Black Hole: Heat Engine

Topological classification of critical points for hairy black holes in Lovelock gravity

In various fields of mathematical research, the Brouwer degree is a potent tool for topological analysis. By using the Brouwer degree defined in one-dimensional space, we interpret the equation of state for temperature in black hole thermodynamics, T=T(V,xi), as a spinodal curve, with its derivative defining a new function f. The sign of the slope of f indicates the topological charge of the black hole’s critical points, and the total topological charge can be deduced from the asymptotic behavior of the function f. We analyze a spherical hairy black hole within the framework of Lovelock gravity, paying particular attention to the topological structure of black hole thermodynamics under Gauss–Bonnet gravity. Here, the sign of the scalar hair parameter influences the topological classification of uncharged black holes. When exploring the thermodynamic topological properties of hairy black holes under cubic Lovelock gravity, we find that the spherical hairy black hole reproduces the thermodynamic topological classification results seen under Gauss–Bonnet gravity.

Schottky Anomaly of the Kalb-Ramond-de Sitter Spacetime

In the theory of gravity, the spontaneous breaking of Lorentz symmetry due to the non-minimal coupling between the Kalb-Ramond field and Einstein gravity results in the existence of exactly static and spherically symmetric black hole solutions related to the Lorentz violating parameter. Based on the consideration of the interaction between the black hole and cosmological horizons, this paper studies the thermodynamic properties of Kalb-Ramond-de Sitter (KR-dS) spacetime. The Smarr relation expressed by equivalent thermodynamic quantities is found, and it is proved that the equivalent thermodynamic quantities of the KR-dS spacetime satisfy the universal Euler's theorem. It is discovered that the heat capacity of the KR-dS spacetime with respect to the ratio of the two horizons and the variation curve of the heat capacity with effective temperature possess the characteristics of Schottky specific heat. Moreover, the black hole and the cosmological horizon in the equivalent thermodynamic system are regarded as two different energy levels, and the heat capacity of the KR-dS spacetime is discussed using the general form given by the ordinary two-level system. It is found that the heat capacity of KR-dS spacetime described by equivalent thermodynamic quantities not only conforms to the characteristics of Schottky specific heat but also is consistent with the heat capacity of the ordinary two-level system. This result reflects that when the cosmological constant and the charged carried in the KR-dS spacetime remain unchanged, the heat capacity of the system can be represented by a universal two-level system. By comparing the maximum value of the heat capacity curves, the number of microscopic particles between the two horizons can be estimated, which reflects the quantum properties of the KR-dS spacetime. These studies will open a new perspective to probe the thermodynamics of black holes.