Black Hole Entropy Research Articles

On separable states in relativistic quantum field theory

We initiate an investigation into separable, but physically reasonable, states in relativistic quantum field theory. In particular we will consider the minimum amount of energy density needed to ensure the existence of separable states between given spacelike separated regions. This is a first step towards improving our understanding of the balance between entanglement entropy and energy (density), which is of great physical interest in its own right and also in the context of black hole thermodynamics. We will focus concretely on a linear scalar quantum field in a topologically trivial, four-dimensional globally hyperbolic spacetime. For rather general spacelike separated regions A and B we prove the existence of a separable quasi-free Hadamard state. In Minkowski spacetime we provide a tighter construction for massive free scalar fields: given any R > 0 we construct a quasi-free Hadamard state which is stationary, homogeneous, spatially isotropic and separable between any two regions in an inertial time slice all of whose points have a distance . We also show that the normal ordered energy density of these states can be made (in Planck units). To achieve these results we use a rather explicit construction of test-functions f of positive type for which we can get sufficient control on lower bounds on .

Extended phase space thermodynamics for hairy black holes

Extended phase space thermodynamics for hairy black holes

Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity

In this letter, we present the first study of Hawking radiation as a tunneling process within the framework of non-commutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole (NC SBH) within the gauge theory of gravity, employing the Seiberg-Witten (SW) map and the star product. Then, we compute the emission spectrum of outgoing massless particles using the quantum tunneling mechanism. In the first scenario, we calculate the tunneling rate of massless particles crossing the event horizon of the NC SBH with lower frequencies. Our results reveal pure thermal radiation. Notably, we find that the Hawking temperature remains consistent in both the classical thermodynamics and the quantum tunneling approach, suggesting equivalence between these two approaches in NC spacetime. However, in the case of massless particle emission with higher frequencies, we account for energy conservation resulting in the tunneling rate to deviate from pure thermal radiation. This tunneling rate remains consistent with an underlying unitary quantum theory. We establish a relationship between this deviation and the change in the black hole entropy, revealing a logarithmic correction to the entropy within this geometry. Furthermore, we demonstrate that non-commutativity enhances the correlations between two successively emitted particles. Additionally, we determine the NC density number of particle emission and conclude by discussing the implications of our findings.

Thermodynamics of charged accelerating AdS black hole

In this paper, we provide a thermodynamical study of charged accelerating AdS black holes in the [Formula: see text]-metric. In this connection, we first determine the mass of the given black hole and study their dependence on horizon radius and acceleration. Furthermore, following black hole mechanics, we also derive various quantities like Hawking temperature, entropy, pressure, volume, internal energy, Gibbs energy and Helmholtz energy. With the help of a graph, we study the effect of acceleration on these thermal quantities. Here, we observe that the impact of acceleration becomes more significant on the large horizons. To discuss stability and phase transition, we calculate specific heat. The graphical analysis suggests multiple phase transitions occur for the charged accelerating black hole in AdS spacetime. The system changes state at the critical point, where phase transition occurs. For the small black holes, the critical point at which the phase transition occurs is independent of the acceleration parameter. However, the critical horizon radius for large black holes depends on the acceleration parameter. For fast-accelerating black holes, a phase transition occurs at a small horizon radius to that of slowly accelerating black holes.

Supersymmetric Cardy formula and the Weak Gravity Conjecture in AdS/CFT

The Weak Gravity Conjecture (WGC) in anti-de Sitter spacetime (AdS) asserts the existence of an operator in the boundary conformal field theory (CFT) whose scaling dimension-to-charge ratio satisfies a certain upper bound. This bound is specified by the ratio of the conformal central charge c and the flavor central charge kF. We propose a modified bound in AdS5/CFT4, determined by a combination of two central charges 3c − 2a instead of c. This combination arises in the Cardy-like limit of the 4d superconformal index, which captures the Bekenstein-Hawking entropy of large BPS black holes in AdS5. Using the new bound, we find that certain superconformal field theories (SCFTs) that are previously thought to violate the AdS WGC, including SQCDs in the conformal window, do satisfy the WGC. We check this version of the WGC against all possible superconformal gauge theories with SU(N) gauge group admitting a large N limit when the superpotential is absent. We conjecture the modified version of the WGC is a generic property of any 4d SCFT, regardless of the existence of a weakly coupled gravity dual or a large N limit.

Entropy-current for dynamical black holes in Chern-Simons theories of gravity

We construct an entropy current and establish a local version of the classical second law of thermodynamics for dynamical black holes in Chern-Simons (CS) theories of gravity. We work in a chosen set of Gaussian null coordinates and assume the dynamics to be small perturbations around the Killing horizon. In explicit examples of both purely gravitational and mixed gauge gravity CS theories in (2 + 1) and (4 + 1)-dimensions, the entropy current is obtained by studying the off-shell structure of the equations of motion evaluated on the horizon. For the CS theory in (2 + 1) dimensions, we argue that the second law holds to quadratic order in perturbations by considering it as a low energy effective field theory with the leading piece given by Einstein gravity. In all such examples, we show that the construction of entropy current is invariant under the reparameterization of the null horizon coordinates. Finally, extending an existing formalism for diffeomorphism invariant theories, we construct an abstract proof for the linearised second law in arbitrary Chern-Simons theories in any given odd dimensions by studying the off-shell equations of motion. As a check of consistency, we verify that the outcome of this algorithmic proof matches precisely with the results obtained in explicit examples.

Cosmological LTB black hole in a quintom universe

We study cosmological Lemaitre–Tolman–Bondi (LTB) black hole thermodynamics immersed in a quintom universe. We investigate some thermodynamic aspects of such a black hole in detail. We apply two methods of treating particles’ tunneling from the apparent horizons and calculate the black hole’s temperature in each method; the results of which are the same. In addition, by considering specific time slices in the cosmic history, we study the thermodynamic features of this black hole in these specific cosmic epochs. Also, we discuss the information loss problem and the remnant content of the cosmological black hole in different cosmic epochs in this context. We show that approximately in all the cosmic history, the temperature of the black hole’s apparent horizon is more than the temperature of the cosmological apparent horizon.

A regular black hole as the final state of evolution of a singular black hole

We propose a novel black hole model in which singular and regular black holes are combined as a whole and more precisely singular and regular black holes are regarded as different states of parameter evolution. We refer to them as singular and regular states, respectively. Furthermore, the regular state is depicted by the final state of parameter evolution in the model. We also present the sources that can generate such a black hole spacetime in the framework of F(R) gravity. This theory of modified gravity is adopted because it offers a possible resolution to a tough issue in the thermodynamics of regular black holes, namely the discrepancy between the thermal entropy and Wald entropy. The dynamics and thermodynamics of the novel black hole model are also discussed when a singular state evolves into a regular state during the change of charge or horizon radius from its initial value to its extreme value.

From giant gravitons to black holes

We study AdS5 black holes from a recently suggested giant graviton expansion formula for the index of U(N) maximal super-Yang-Mills theory. We compute the large N entropy at fixed charges and giant graviton numbers nI by a saddle point analysis, and further maximize it in nI. This agrees with the dual black hole entropy in the small black hole limit. To get black holes at general sizes, one should note that various giant graviton indices cancel because gauge theory does not suffer from a Hagedorn-like pathology by an infinite baryonic tower. With one assumption on the mechanism of this cancellation, we account for the dual black hole entropy at general sizes. We interpret our results as analytic continuations of the large N free energies of SCFTs, and based on it compute the entropies of AdS4,7 black holes from M5, M2 giant gravitons.

Negative corrections to black hole entropy from string theory

Negative corrections to black hole entropy from string theory

Einstein–Bumblebee-dilaton black hole solution

We obtain new black hole solutions in a Einstein–Bumblebee-scalar theory. By starting with a Einstein–Bumblebee theory in (D+d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D+d$$\\end{document}) dimensions, the scalar dilaton field and its interaction with the gravitational and Bumblebee fields are obtained by Kaluza–Klein (KK) reduction over the extra dimensions. Considering the effects of both the Bumblebee vacuum expectation value (VEV) and the fluctuations over the VEV, we obtained new charged solutions in (3+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(3+1)$$\\end{document} dimensions. For a vanishing dilaton, the black hole turned out to be a charged de Sitter-Reissner–Nordstrom solution, where the transverse mode is the Maxwell field and the longitudinal mode is the cosmological constant. The stability of these new solutions is investigated by means of the analysis of the black hole thermodynamics. The temperature, entropy, and heat capacity show that these modified black holes are thermodynamic stable.

Thermodynamics of a quantum corrected Reissner-Nordström black hole

In the modified Reissner-Nordström (RN) black hole with quantum excitations of spacetime, we investigate the quantum corrected thermodynamics. First, we calculate the thermodynamic quantities and examine the quantum corrections on the temperature, entropy and heat capacity. To ensure the black hole mass having the basic physics meaning, we obtain the critical state with Planck scale. Letting the thermal capacity equal zero, we derived the radiation remnant which is consistent with the critical state. Also, we analyze the thermal capacity and discuss the thermal stability of the black hole. Next, using the quantum tunneling method and taking into account the second-order WKB approximation, we calculate the tunneling probability of massless particle. It is found that the tunneling rate is regularized by the quantum excitations of spacetime. As well as, for the tunneling radiation, there are correlations between the emitted modes and holds the potential to address the black hole information loss problem. Besides, based on the unitary of the quantum tunneling, we obtained the corrected black hole entropy, which contains the logarithm and inverse of the black hole area.

Quantum tunneling of spin-1/2 and spin-3/2 particles in the black holes of asymptotically safe gravity

Hawking initiated study of radiations from black holes. The black hole thermodynamics holds a significant importance in understanding of quantum nature of gravity. In this article, Hawking radiations have been studied by employing the semi-classical perspective of quantum tunneling. Dirac and Rarita-Schwinger equations have been employed to determine the tunneling probabilities of spin-1/2 and spin-3/2 particles, respectively, in the background of black holes developed in the asymptotically safe gravity. Hawking temperature determined in both cases is in agreement.

The chaotic behavior of black holes: Investigating a topological retraction in anti-de Sitter spaces

In some topological universe models, a special type of curved space called the anti-de Sitter (AdS) of black hole space appears. Due to general relativity, this space has negative curvature. Here we present a novel variant of AdS space, known as chaotic AdS black hole space. We investigate the correlation between the folding of chaotic AdS black hole space and its chaotic deformation retract. In order to better understand how objects move in space, we can also use Lagrangian equations to determine the geodesics of the chaotic AdS space, and explore the properties and behavior of this new type of space. This would enable us to focus our attention and efforts better on black hole thermodynamics and quantum gravity. Finally, various types of chaotic quantum retractions in this space are identified, as well as the final limits on chaotic AdS spaces and their extensions to astrophysics. Exploring these ideas has consequently increased our understanding of the complex dynamics of the universe and the potential for developing a theory of quantum gravity that combines the principles of general relativity and quantum mechanics.

Thermodynamics and evaporation of perfect fluid dark matter black hole in phantom background

We present a novel interpretation of the thermodynamics of perfect fluid dark matter (PFDM) black hole based on Misner–Sharp energy and then investigate its evaporation behavior. We find that the ratio between dark sector initial density and black hole horizon radius significantly influences black hole evaporation behaviors. We demonstrate that the presence of the dark sector can significantly extend the lifetime of a black hole which is similar to the Reissner–Nordström case. Our work reformulates the thermodynamics of PFDM black holes and points out the existence of long-lived black holes in the presence of the dark sector.

Black holes and hot shells in the Euclidean path integral approach to quantum gravity

We study a spherical black hole surrounded by a hot self-gravitating thin shell in the canonical ensemble, i.e. a black hole and a hot thin shell inside a heat reservoir acting as a boundary with its area and temperature fixed. To work out the quantum statistical mechanics partition function of this matter-black hole system, from which the thermodynamics of the system follows, we use the Euclidean path integral approach to quantum gravity that identifies the path integral of the gravitational system with the partition function itself. In a semiclassical evaluation of the path integral, one needs to compute the classical action of the system. From the action, one finds the result that the total entropy, given by the sum of black hole and matter entropies, is a function of the gravitational radius of the system alone. So, the black hole inside the shell has no direct influence on the total entropy. One also finds the free energy which is equal to the action times the temperature, the thermodynamic energy, and the temperature stratification along the system. Another important result is that the heat reservoir temperature is composed of a free function of the gravitational radius of the system, which acts as a reduced temperature equation of state, divided by the redshift function at the reservoir. Upon the specification of the reduced temperature, the solutions for the gravitational radii of the system compatible with the boundary data can be found. In addition, it is found that the black hole inside the shell has two possible horizon radii. The first law of thermodynamics is then identified, and it is shown that the first law is satisfied by the system as whole, it is realized by the matter in the hot shell, and it is also applicable to the black hole. The thermodynamic stability analysis is performed through the calculation of the system’s heat capacity. By specifying the available temperature free function as the Hawking temperature equation of state of the gravitational radius of the system, which itself is not a black hole, one finds a remarkable exact mechanical and thermodynamic solution. With the exact solution in hand one establishes that pure black hole spaces, hot shell with a black hole spaces, pure hot shell spaces, and hot flat spaces are phases that cohabit in the ensemble, with some of them acting as thermodynamic mimickers. This exact thermodynamic solution for a black hole with a self-gravitating hot shell is not only of interest in itself, but can also be seen as a model to situations involving black holes interacting with hot gravitons and other hot particles. The study of the high temperature limits for the system also reveals several important aspects.

Testing the Minimum System Entropy and the Quantum of Entropy.

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature.

AdS Black Hole Thermodynamics and Microstructures from f(Q)$f(Q)$ Gravitation

AbstractThe significant properties and phase transition of charged Anti‐de Sitter (AdS) black holes have been extensively studied in a variety of modified theories of gravity in the presence of numerous matter fields. The goal of the current research is to investigate the AdS black hole's thermodynamics under the impact of gravity. Additionally, this paper explores the black hole's local stability and phase structure under the relevant gravity. Besides, Ruppeiner geometry is used to look into the AdS black hole's microscopic structure. The Ricci curvature scalar R to explain the interactions between the AdS black hole's microscopic particles under the influence of gravity have been numerically computed.

Thermodynamics of novel scalar–tensor-Born–Infeld black holes

Two novel classes of four-dimensional exact black hole (BH) solutions have been obtained in the scalar–tensor (ST) theory which are coupled to Born–Infeld (BI) electrodynamics. To this end, a conformal transformation (CT) has been applied which transforms the action of ST–BI gravity to that of Einstein–dilaton–BI theory. The scalar-coupled BI theory, which has been introduced here, slightly differs from those have been used, previously. The analytical solutions have been obtained in the Einstein frame (EF) and two classes of charged dilatonic BHs, with unusual asymptotic behaviors, have been presented. All the solutions coincide with the corresponding values of Einstein–dilaton–Maxwell theory, in the limit of large BI parameter. By calculating thermodynamic parameters and, noting the Smarr mass relation, we showed that the first law of BH thermodynamics (FLT) is valid for the novel dilatonic BHs. Stability of the BHs has been investigated in EF, making use of the canonical ensemble method and noting the signature of the BH heat capacity (HC). Next, by use of the inverse CT, the solutions of ST theory have been obtained from their EF counterparts. Although, the entropy of ST BHs violates entropy-area law, the thermodynamic and conserved quantities have been obtained noting their conformal invariance property. It has been found that the ST BHs have the same thermodynamic and stability properties as the Einstein–dilaton ones.

Black hole thermodynamics in Horndeski theories

Black hole thermodynamics in Horndeski theories