A universal relation between the leading correction to the entropy and extremality was gotten in the work of Goon and Penco. In this paper, we extend this work to the massive gravity and investigate thermodynamic extremality relations in a topologically higher-dimensional black hole. A rescaled cosmological constant is added to the action of the massive gravity as a perturbative correction. This correction modifies the extremality bound of the black hole and leads to the shifts of the mass, entropy, etc. The Goon-Penco relation is gotten. Regarding the cosmological constant as a variable related to pressure, we get the thermodynamic extremality relations between the mass and pressure, charge, parameters $c_i$ by accurate calculations, respectively. Finally, these relations are verified by a triple product identity, which shows that the universal relation exists in black holes.
It is argued that many non-extremal black branes exhibit a classical Gregory-Laflamme instability if, and only if, they are locally thermodynamically unstable. For some black branes, the Gregory-Laflamme instability must therefore disappear near extremality. For the black $p$-branes of the type II supergravity theories, the Gregory-Laflamme instability disappears near extremality for $p=1,2,4$ but persists all the way down to extremality for $p=5,6$ (the black D3-brane is not covered by the analysis of this paper). This implies that the instability also vanishes for the near-extremal black M2 …
The universal thermodynamic relations between corrections to entropy and extremality for various black holes solutions have been studied. In this regard, we hereby consider a number of different black brane solutions in different structures for perturbative corrections to general relativity. These are, namely, black brane solution in Rastall AdS massive gravity, Einstein-Yang-Mills AdS black brane solution in massive gravity and general anisotropic black brane in Horava-Lifshitz gravity. We calculate both the entropy and extremality bound by introducing a small constant correction to the actio…
The perturbation correction of general relativity has obtained the general relationship between entropy and extremality. The relation was found to exactly hold for the charged AdS black hole, and extended to the rotating and massive gravity black holes. In this paper, We confirm the universal relation for the four dimensional RN-AdS black hole surrounded by the quintessence, and find a new extremality relation between black hole mass and the normalization factor $a$ related to the density of quintessence. Besides, we also find that when the black hole entropy increases, the correction constant…
Perturbative corrections to General Relativity alter the expressions for both the entropy of black holes and their extremality bounds. We prove a universal relation between the leading corrections to these quantities. The derivation is purely thermodynamic and the result also applies beyond the realm of gravitational systems. In scenarios where the correction to the entropy is positive, our result proves that the perturbations decrease the mass of extremal black holes, when holding all other extensive variables fixed in the comparison. This implies that the extremality relations of a wide clas…
In [Phys. Rev. Lett. 124, 101103 (2020)], a universal relation between corrections to entropy and extremality was proposed. The relation was also found to exactly hold for the four-dimensional charged AdS black hole. In this paper, we extend the study to the rotating BTZ and Kerr-AdS black holes when a constant correction to General Relativity is considered for the first time. The entropy and extremality bound are calculated, and they have a closely dependent behavior with the coupling parameter of the constant correction. We confirm the universal relation for the rotating AdS black holes. Fur…
We test whether static charged dilaton black holes in 2+1 dimensions can be turned into naked singularities, by sending in test particles from infinity. We derive that overcharging is possible and generic for both extremal and nearly extremal black holes. Our analysis also imply that nearly extremal charged dilaton black holes can be continuously driven to extremality and beyond, unlike nearly extremal Baunados-Teitelboim-Zanelli, Kerr and Reissner-Nordström black holes which are overspun or overcharged by a discrete jump. Thus the weak form of the cosmic censorship conjecture and the third la…
We study a two-dimensional theory of gravity coupled to matter that is relevant to describe holographic properties of black holes with a single rotational parameter in five dimensions (with or without cosmological constant). We focus on the near-horizon geometry of the near-extremal black hole, where the effective theory reduces to Jackiw-Teitelboim (JT) gravity coupled to a massive scalar field. We compute the corrections to correlation functions due to cubic interactions present in this theory. A novel feature is that these corrections do not have a definite sign: for AdS$_5$ black holes the…
We develop the thermodynamics of BPS and near-BPS AdS6 black holes. We study the phase diagram of BPS black holes in the grand canonical ensemble. We highlight two distinct deformations orthogonal to the BPS surface: (i) increasing the temperature while keeping the charges fixed, (ii) changing the charges while maintaining extremality such that the BPS constraint is no longer satisfied. For both these deformations, we show that the considerations of the BPS entropy function can be extended to describe the near-BPS regime. The excess entropy together with changes in all potentials are perfectly…
We investigate thermodynamic curvatures of the Kerr and Reissner-Nordström (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for $d=5$ Kerr black hole is curved and divergent in the extremal limit. For $d \geq 6$ Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geomet…
The cosmic censorship conjecture essentially states that naked singularities should not form from generic initial conditions. Since black hole parameters can change their values under Hawking evaporation, one has to ask whether it is possible to reach extremality by simply waiting for the black hole to evaporate. If so a slight perturbation would likely render the singularity naked. Fortunately, at least for the case of asymptotically flat 4-dimensional Reissner-Nordström black hole, Hiscock and Weems showed that it can never reach extremality despite the fact that for a sufficiently massive b…
We investigate the weak cosmic censorship conjecture in charged anti-de Sitter black holes with thermodynamic pressure and volume by the scattering of the charged scalar field in four and higher dimensions. We assume that the internal energy and electric charge of the black hole changes infinitesimally according to the energy and charge fluxes of the scalar field. Then, found to be an isobaric process, the changes in the black hole can be well reproduced to the first law of thermodynamics, although we find that the second law of thermodynamics is violated in extremal and near-extremal black ho…
We explore the BPS limit of asymptotically flat black hole thermodynamics, drawing analogies with recent studies of black holes in anti-de Sitter space. Although ultimately motivated by supersymmetry and quantum gravity, the BPS limit is classically well-defined for the dyonic Kerr-Newman black holes in pure Einstein-Maxwell theory and various generalizations with additional scalars and gauge fields that admit embedding in $\mathcal{N}=2$ supergravity (for concreteness we consider the STU model). This limit is manifestly different from extremality as it includes a family of rotating Euclidean …
We construct non-extremal dyonic string solutions in 6D minimal supergravity where the leading higher derivative corrections arise from either the type IIA string theory compactified on K3 or the heterotic string theory compactified on 4-torus. The thermodynamical quantities and Euclidean actions of the strings are computed. In the near extremal regime, we calculate the force felt by a probe fundamental string in the background of the macroscopic dyonic string with leading $α'$ corrections. We find that in both the IIA and heterotic setups, away from extremality, the attractive force overwhelm…
We study the geodesic motion of massive and massless test particles in the background of equally spinning Myers-Perry-anti-de Sitter (AdS) black holes in five dimensions. By adopting a coordinate system that makes manifest the cohomogeneity-1 property of these spacetimes, the equations of motion simplify considerably. This allows us to easily separate the radial motion from the angular part and to obtain solutions for angular trajectories in a compact closed form. For the radial motion we focus our attention on spherical orbits. In particular, we determine the timelike innermost stable circula…
In this work we attempt to overcharge extremal and nearly extremal charged black holes in string theory, known as the Garfinkle-Horowitz-Strominger solution. We first show that extremal black holes cannot be overcharged analogous to the case of Reissner-Nordström black holes. Contrary to their analogues in general relativity, nearly extremal black holes can neither be overcharged beyond extremality, nor can they be driven to extremality by the interaction with test particles. Therefore the analysis in this work also imply that the third law of black hole thermodynamics holds for the relevant c…
We revisit the general topic of thermodynamical stability and critical phenomena in black hole physics, analyzing in detail the phase diagram of the five dimensional rotating black hole and the black rings discovered by Emparan and Reall. First we address the issue of microcanonical stability of these spacetimes and its relation to thermodynamics by using the so-called Poincare (or "turning point") method, which we review in detail. We are able to prove that one of the black ring branches is always locally unstable, showing that there is a change of stability at the point where the two black r…
In this paper we investigate the thermodynamic properties of the stationary Lifshitz black hole solution of New Massive Gravity. We study the thermodynamic stability from local and global point of view. We also consider the space of equilibrium states for the solution within the framework of Thermodynamic Information Geometry. By investigating the proper thermodynamic metrics and their curvature invariants we find a set of restrictions on the parameter space and the critical points indicating phase transitions of the system. We confirm our findings by analytical analysis of the geodesics on th…
We show that the decay spectrum of massive excitations in perturbative string theories is thermal when averaged over the (many) initial degenerate states. We first compute the inclusive photon spectrum for open strings at the tree level showing that a black body spectrum with the Hagedorn temperature emerges in the averaging. A similar calculation for a massive closed string state with winding and Kaluza-Klein charges shows that the emitted graviton spectrum is thermal with a "grey-body" factor, which approaches one near extremality. These results uncover a simple physical meaning of the Haged…
Recent results of quantum field theory on a curved spacetime suggest that extremal black holes are not thermal objects and that the notion of zero temperature is ill-defined for them. If this is correct, one may have to go to a full semiclassical theory of gravity, including backreaction, in order to make sense of the third law of black hole thermodynamics. Alternatively, it is possible that we shall have to drastically revise the status of extremality in black hole thermodynamics.
The approximate renormalized stress-energy tensor of the quantized massive conformally coupled scalar field in the spacetime of electrically charged nonlinear black hole is constructed. It is achieved by functional differentiation of the lowest order of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficient $a_{3}.$ The result is compared with the analogous result derived for the Reissner-Nordström black hole. It is shown that the most important differences occur in the vicinity of the event horizon of the black hole near the…
Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive cosmological model proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation $δQ=T dS$, the modified Fri…
We investigate the tendency in variations of the dual CFT$_2$ when a rotating AdS$_3$ black hole changes by fluxes transferred by the scattering of a massive scalar field according to the AdS/CFT correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities, so the black hole cannot be extremal under the scattering. This is naturally preferred. By the relationship between the rotating AdS$_3$ black hole and dual CFT$_2$, we find that such chang…
In this paper, we consider the Einstein-massive gravity coupled to the Yang-Mills gauge field in five dimensions. Concentrating on the static solutions with planar horizon geometry, we explore the thermodynamic behavior in the extended phase space and examine the validity of the first law of thermodynamics besides local thermal stability by the Hessian matrix. We observe that although the topology of boundary is planar, there exists the van der Waals like phase transition for this kind of solution. We find the critical quantities and discuss how the massive and Yang-Mills parameters affect the…
In three dimensions, we consider the Einstein-Maxwell Lagrangian dressed by a nonminimally coupled scalar field in New Massive Gravity. For this theory, we provide two families of electrically charged Lifshitz black holes where their metric functions depend only on an integration constant. We calculate their masses using the quasilocal approach, as well as their entropy and electric charge. These charged configurations are interpreted as extremal in the sense that the mass vanishes identically while the entropy and electric charge are non zero thermodynamic quantities. Using these examples, we…
Following earlier study regarding Einstein-Gauss-Bonnet-massive black holes in the presence of Born-Infeld nonlinear electromagnetic field [S. H. Hendi, B. Eslam Panah and S. Panahiyan, arXiv:1510.00108], we study thermodynamical structure and critical behavior of these black holes through various methods in this paper. Geometrical thermodynamics is employed to give a picture regarding phase transition of these black holes. Next, a new method is used to derive critical pressure and horizon radius of these black holes. In addition, Maxwell equal area law is employed to study the Van der Waals l…
A version of massive gravity, namely conformal massive gravity, is employed to study the behavior of thermodynamic geometry for both the static and the rotating regular black holes. Whereas in thermodynamic geometry singularity can be interpreted as the second phase transition, seeing such phenomena as heat capacity behavior for both cases is investigated in detail. In addition, other thermodynamic quantities like the entropy and the temperature are analyzed as well. Another important property of the black holes is the so-called stability, in which utilizing the first phase transition of the h…
We consider the generalized laws of thermodynamics in massive gravity. Making use of explicit black hole solutions, we devise black hole merger processes in which i) total entropy of the system decreases ii) the zero-temperature extremal black hole is created. Thus, both second and third laws of thermodynamics are violated. In both cases, the violation can be traced back to the presence of negative-mass black holes, which, in turn, is related to the violation of the null energy condition. The violation of the third law of thermodynamics implies, in particular, that a naked singularity may be c…
Testing the Weak Gravity Conjecture via Gravitational Lensing, Black Hole Shadows, and Barrow Thermodynamics in F(R)-Euler-Heisenberg (A)dS Black Holes
Damghan University（达姆甘大学）；Eastern Mediterranean University（东地中海大学）；University of Mazandaran（马赞德兰大学）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Canadian Quantum Research Center（加拿大量子研究中心）；Khazar University（哈扎尔大学）
We study the near-horizon AdS_2\timesS^2 geometry of evaporating near-extremal Reissner-Nordstrom black holes interacting with null matter. The non-local (boundary) terms t_{\pm}, coming from the effective theory corrected with the quantum Polyakov-Liouville action, are treated as dynamical variables. We describe analytically the evaporation process which turns out to be compatible with the third law of thermodynamics, i.e., an infinite amount of time is required for the black hole to decay to extremality. Finally we comment briefly on the implications of our results for the information loss p…
Logarithmic corrections to the entropy of near-extremal black holes in New Massive Gravity
Instituto de Física La Plata (IFLP), CONICET & Departmento de Física Dr. Emil H. Bose, UNLP（拉普拉塔物理研究所（IFLP），阿根廷国家科学研究委员会 & 恩里克·H·博塞物理学系，拉普拉塔国立大学）；Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México（物理系，理学院，墨西哥国立自治大学）；Departamento de Física, Universidad de Concepción（物理系，孔塞普西翁大学）；Instituto de Astronomía y Física del Espacio, (CONICET-UBA)（天体物理学与空间物理研究所（阿根廷国家科学研究委员会-布宜诺斯艾利斯大学））
In this paper, we investigate the tunneling process of charged massive bosons $W^{\pm }$ (spin-1 particles) from noncommutative charged black holes such as charged RN black holes and charged BTZ black holes. By applying the WKB approximation and by using the Hamilton-Jacobi equation we derive the tunneling rate and the corresponding Hawking temperature for those black holes configuration. Furthermore, we show the quantum gravity effects using the GUP on the Hawking temperature for the noncommutative RN black holes. The tunneling rate shows that the radiation deviates from pure thermality and i…
We numerically reanalyze static and spherically symmetric black hole solutions in an Einstein-Maxwell-dilaton system with a dilaton potential $m_{d}^{2}ϕ^{2}$. We investigate thermodynamic properties for various dilaton coupling constants and find that thermodynamic properties change at a critical dilaton mass $m_{d,crit}$. For $m_{d}\geq m_{d,crit}$, the black hole becomes an extreme solution for a nonzero horizon radius $r_{h,ex}$ as the Reissner-Nordström black hole. However, if $m_{d}$ is nearly equal to $m_{d,crit}$, there appears a solution of smaller horizon radius than $r_{h,ex}$. For …
Motivated by providing preliminary steps to understand the conception of quantum gravity, in this paper, we study the phase structure of a semiclassical gravitational system. We investigate the stability conditions and phase transition of charged black holes in massive gravity via canonical and geometrical thermodynamic approaches. We point out the effects of massive parameter on stability conditions of these black holes and show how massive coefficients affect the phase transition points of these black holes. We also study the effects of boundary topology on thermodynamical behavior of the sy…
The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is a modification of the Schwarzschild black hole. We present the Bardeen black hole solution in the presence of the de Rham, Gabadaadze, and Tolly (dRGT) massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution reduces to the Bardeen black hole in the absence of a massive gravity parameter, and the Schwarzschild black hole when magnetic charge $g = 0$. We investigated the thermodynamic quantities, that is, mass (…
In this paper, we study massive gravity in the presence of Born-Infeld nonlinear electrodynamics. First, we obtain metric function related to this gravity and investigate the geometry of the solutions and find that there is an essential singularity at the origin ($r=0$). It will be shown that due to contribution of the massive part, the number, types and places of horizons may be changed. Next, we calculate the conserved and thermodynamic quantities and check the validation of the first law of thermodynamics. We also investigate thermal stability of these black holes in context of canonical en…
We derive new bounds on higher-dimension operator coefficients in four-dimensional Einstein-Maxwell theory. Positivity of classically-generated corrections to the Wald entropy of thermodynamically stable, rotating dyonic black holes implies a multiparameter family of field basis invariant inequalities that exhibit electromagnetic duality and are satisfied by examples from field and string theory. These bounds imply that effective operators modify the extremality condition of large black holes so as to permit their decay to smaller ones, thus satisfying the weak gravity conjecture.
We study the extended phase space thermodynamics of black holes in massive gravity. Particularly, we examine the critical behaviour of this black hole using the extended phase space formalism. Extended phase space in a sense that in which the cosmological constant should be treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. In this phase space, we derive the black hole equation of state, the critical pressure, the critical volume and the critical temperature at the critical point. We also derive the critical ratio of this black hole. Moreover, we derive t…
Motivated by high interest in the close relation between string theory and black hole solutions, in this paper, we take into account the Einstein-Gauss-Bonnet Lagrangian in the context of massive gravity. We examine the possibility of black hole in this regard, and discuss the types of horizons. Next, we calculate conserved and thermodynamic quantities and check the validity of the first law of thermodynamics. In addition, we investigate the stability of these black holes in context of canonical ensemble. We show that number, type and place of phase transition points may be significantly affec…
Violation of Lorentz invariancy in the high energy quantum gravity motivates one to consider an energy dependent spacetime with massive deformation of standard general relativity. In this paper, we take into account an energy dependent metric in the context of a massive gravity model to obtain exact solutions. We investigate the geometry of black hole solutions and also calculate the conserved and thermodynamic quantities, which are fully reproduced by the analysis performed with the standard techniques. After examining the validity of the first law of thermodynamics, we conduct a study regard…
Motivated by gauge/gravity group in the low energy effective theory of the heterotic string theory and novel aspects of massive gravity in the context of lattice physics, the minimal coupling of Gauss-Bonnet-massive gravity with Born-Infeld electrodynamics is considered. At first, the metric function is calculated and then the geometrical properties of the solutions are investigated. It is found that there is an essential singularity at the origin and the intrinsic curvature is regular elsewhere. In addition, the effects of massive parameters are studied and black hole solutions with multi hor…
We discuss the use of information geometry in black hole physics and present the outcomes. The type of information geometry we utilize in this approach is the thermodynamic (Ruppeiner) geometry defined on the state space of a given thermodynamic system in equilibrium. The Ruppeiner geometry can be used to analyze stability and critical phenomena in black hole physics with results consistent with those from the Poincare stability analysis for black holes and black rings. Furthermore other physical phenomena are well encoded in the Ruppeiner metric such as the sign of specific heat and the extre…
We consider an Einstein-Gauss-Bonnet massive gravity model in $4D$ AdS spacetime to obtain a possible black hole solution and discuss the horizon structure of this black hole. The real roots of the vanishing metric function lead to various types of horizons. Furthermore, we derive various thermodynamic quantities, thus insuring the validity of the first-law of thermodynamics and the Smarr relation. The thermodynamic quantities are modified in the presence of the massive gravity parameter and also discuss the stability of the system from the heat capacity. Black hole space times can not only po…
We consider the two classes cosh and sinh of normal and phantom black holes of Einstein-Maxwell-dilaton theory. The thermodynamics of these holes is characterized by heat capacities that may have both signs depending on the parameters of the theory. Leaving aside the normal Reissner-Nordström black hole, it is shown that only some phantom black holes of both classes exhibit critical phenomena. The two classes share a nonextremality, but special, critical point where the transition is continuous and the heat capacity, at constant charge, changes sign with an infinite discontinuity. This point y…
Thermodynamic stability and geometric thermodynamics of charged black holes in Rastall-massive gravity under quintessence
Cadi Ayyad University（卡迪阿雅德大学）；National School of Applied Sciences（国立应用科学学院）；Centre Regional des Metiers de l’Education et de la Formation de Marrakech（马拉喀什地区教育与职业培训中心）
Starting from the Frolov-Zel'nikov stress-energy tensor of quantum massive fields in the Schwarzschild background, we recover the contribution $S_{q}$ of these field into the entropy of a black hole. For fermions with the spin $%s=1/2$ $S_{q}>0$, for scalar fields $S_{q}>0$ provided the coupling parameter is restricted to some interval, and $S_{q}<0$ for vector fields. The appearance of negative values of $S_{q}$ is attributed to the fact that in the situation under discussion there are no real quanta to contribute to the entropy, so $S_{q}$ is due to vacuum polarization entirely and has nothi…
The thermodynamic properties of a static and spherically symmetric hairy black hole solution arising in massive gravity with spontaneous Lorentz breaking are investigated. The analysis is carried out by enclosing the black hole in a spherical cavity whose surface is maintained at a fixed temperature $T$. It turns out that the ensemble is well-defined only if the "hair" parameter $Q$ characterizing the solution is conserved. Under this condition we compute some relevant thermodynamic quantities, such as the thermal energy and entropy, and we study the stability and phase structure of the ensemb…
