In this summary, we present the main topics of the talks presented in the parallel session "Black holes - 5" of the 14th Marcel Grossmann Meeting held in Rome, Italy in July 2015. We first present a short review of the main approaches used to understand thermodynamics by using differential geometry. Then, we present a brief summary of each presentation, including some general remarks and comments.
We study thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization, and does not favor the Bousso-Hawking normalization.
We study thermodynamic quantities and examine the stability of a black hole in a cavity inspired by the noncommutative geometry. It turns out that thermodynamic behavior of the noncommutative black hole is analogous to that of the Reissner-Nordström black hole in the near extremal limit. Moreover, we identify the noncommutative parameter with the squared electric charge with some constants.
We study the thermodynamic properties of the black hole derived in Hořava-Lifshitz (HL) gravity without the detailed-balance condition. The parameter $Ξ=ε^2$ in the HL black hole plays the same role as that of the electric charge in the RN-AdS black hole. By analogy, we treat the parameter $Ξ$ as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy the two black holes have very different thermodynamic properties. By calculating …
In this article, we consider a conventional black hole under f(R) gravity. Due to the small fluctuations around the equilibrium state, we have summarized the expression of the modified thermodynamic entropy of this black hole. At the same time, we also studied the geometric thermodynamics (GTD) of black holes, and studied the adaptability of the curvature scalar of the geometric thermodynamics method to the phase transition point of the black hole. In addition, we also studied the influence of the modified parameters on the thermodynamic behavior of black holes.
On the basis of horizon thermodynamics we study the thermodynamic stability of black holes constructed in general relativity and Gauss-Bonnet gravity. In the framework of horizon thermodynamics there are only five thermodynamic variables $E,P,V,T,S$. It is not necessary to consider concrete matter fields, which may contribute to the pressure of black hole thermodynamic system. In non-vacuum cases, we can derive the equation of state, $P=P(V,T)$. According to the requirements of stable equilibrium in conventional thermodynamics, we start from these thermodynamic variables to calculate the heat …
We assume that the negative cosmological constant as a thermodynamical pressure and the asymptotically anti-de Sitter (AdS) black hole thermodynamics with modified Chaplygin gas. We have written the mass of the black hole, volume, entropy and temperature due to the thermodynamic system. We find a new solution of Einstein's field equations of AdS black hole with modified Chaplygin gas as a thermodynamic system. We also examine the weak, strong and dominant energy conditions for the source fluid of black hole. We also show that the thermodynamic black hole with Chaplygin gas can be considered as…
We study the thermodynamics and the different thermodynamic geometric methods of Reissener-Nordström-de Sitter black hole and its extremal case, which is similar to the de Sitter black hole coupled to a scalar field, rather called an MTZ black hole. While studying the thermodynamics of the systems, we could find some abnormalities. In both cases, the thermodynamic geometric methods could give the correct explanation for the all abnormal thermodynamic behaviors in the system.
Since the temperature of a typical Schwarzschild black hole is very low, some doubts are raised about whether the fluctuations of the black hole can be treated thermodynamically. It is shown that this is not the case: the thermodynamic fluctuations of a black hole are considerably larger than the corresponding quantum fluctuations. Moreover the ratio of the mean square thermodynamic fluctuation to the corresponding quantum fluctuation can be interpreted as a number of the effective constituents of a black hole.
We investigate the thermodynamics of the noncommutative black hole whose static picture is similar to that of the nonsingular black hole known as the de Sitter-Schwarzschild black hole. It turns out that the final remnant of extremal black hole is a thermodynamically stable object. We describe the evaporation process of this black hole by using the noncommutativity-corrected Vaidya metric. It is found that there exists a close relationship between thermodynamic approach and evaporation process.
The null geodesics and the distance of closest approach for photon around a rotating dyonic black hole in $\mathcal{N} = 2, U(1)^2$ gauged supergravity is studied. The phenomenon of black hole shadows with various black hole parameters has also analyzed. Further, the investigation of various thermodynamic properties for this black hole is performed with various thermodynamic parameters at the horizon. The heat capacity to study the thermodynamic stability of this black hole spacetime is also studied. The influence for different values of the black hole parameters $ ν$, $ e $, $ ν$, $ g $ and $…
We study thermodynamic quantities of an acoustic black hole and its thermodynamic stability in a cavity based on the generalized uncertainty principle. It can be shown that there is a minimal black hole which can be a stable remnant after black hole evaporation. Moreover, the behavior of the free energy shows that the large black hole is stable too. Therefore, the acoustic black hole can decay into the remnant or the large black hole.
This paper considers the effects of space noncommutativity on the thermodynamics of a Reissner-Nordström black hole. In the first step, we extend the ordinary formalism of Bekenstein-Hawking to the case of charged black holes in commutative space. In the second step we investigate the effects of space noncommutativity and the generalized uncertainty principle on the thermodynamics of charged black holes. Finally we compare thermodynamics of charged black holes in commutative space with thermodynamics of Schwarzschild black hole in noncommutative space. In this comparison we explore some concep…
Thermodynamical properties of charged AdS black holes with a global monopole still remain obscure. In this paper, we investigate the thermodynamics and phase transition of the black holes in the extended phase space. It is shown that thermodynamical quantities of the black holes exhibit an interesting dependence on the internal global monopole, and they perfectly satisfy both the first law of thermodynamics and Smarr relation. Furthermore, analysis of the local and the global thermodynamical stability manifests that the charged AdS black hole undergoes an elegant phase transition at critical p…
We study the thermodynamics and thermodynamic geometry of Park black hole in Hořava gravity. By incorporating the ideas of differential geometry, we have investigated the thermodynamics using Weinhold geometry and Ruppeiner geometry. We have also analyzed it in the context of newly developed geometrothermodynamics(GTD). Divergence of specific heat is associated with the second order phase transition of black hole. Here in the context of Park black hole, both Weinhold's metric and Ruppeiner's metric well explain this phase transition. But these explanations depend on the choice of potential. He…
We show that, in the framework of Carathéodory's approach to thermodynamics, one can implement black hole thermodynamics by realizing that there exixts a quasi-homogeneity symmetry of the Pfaffian form $\deq$ representing the infinitesimal heat exchanged reversibly by a Kerr-Newman black hole; this allow us to calculate readily an integrating factor, and, as a consequence, a foliation of the thermodynamic manifold can be recovered.
In recent years, the thermodynamic properties of black holes are topics of interests. We investigate the thermodynamic properties like surface gravity and Hawking temperature on event horizon of regular black holes viz. {\it Hayward Class} and {\it asymptotically AdS (Anti-de Sitter)} black holes. We also analyze the {\it thermodynamic volume} and {\it naive geometric volume} of asymptotically AdS black holes and show that the entropy of these black holes is simply the ratio of the naive geometric volume to thermodynamic volume. We plot the different graphs and interpret them physically. We de…
The objective of this paper is to study the thermodynamics and thermodynamic geometry of charged de-Sitter and charged anti de-Sitter black hole solutions in massive gravity. We study the effect of curvature parameter as well as the mass of graviton in the thermodynamics of the black hole system. We further extend our studies to different topology of the space time and its effects on phase transition and thermodynamics. In addition, the phase transition structure of the black hole and its interactions are reproduced using geometrothermodynamics.
The thermodynamical properties of toroidal black holes in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow one to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and specific heat. This black hole is thermodynamically stable and dominates the grand partition function. This means that there is no phase transition, as the one encountered for spherical black holes.
In Parikh and Wilczek's original works, the laws of black hole thermodynamics are not referred and it seems that there is no relation between Hawking radiation via tunnelling and the laws of black hole thermodynamics in their works. However, taking examples for the R-N black hole and the Kerr black hole, we find that they are correlated and even consistent if the tunnelling process is a reversible process.
We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular we analyze its global properties, and extend it to take the entropy of the inner horizon into account. A brief discussion of Kerr-Newman black holes is included.
In contrast to Hawking radiation of black hole with a given spacetime structure, we consider a competitive transition due to a heat transfer from a hotter inner horizon to a colder outer horizon of Kerr black hole, that results in a stable thermodynamical state of extremal black hole. In this process, by supposing an emission of gravitational quanta, we calculate the mass of extremal black hole in the final state of transition.
We study the quasinormal modes of the massless scalar field of Park black hole in the Hořava gravity using the third order WKB approximation method and found that black hole is stable against these perturbation. We compare and discuss the results with that of Schwarzschild-de Sitter black hole. Thermodynamic properties of Park black hole are investigated and the thermodynamic behavior of upper mass bound is also studied.
This paper deals with five-dimensional black hole solutions in (a) Einstein-Yang-Mills-Gauss-Bonnet theory and (b)Einstein-Maxwell-Gauss-Bonnet theory with a cosmological constant for spherically symmetric space time. The geometry of the black hole thermodynamics has been studied for both the black holes.
We investigate the thermodynamic behavior of maximally symmetric charged, asymptotically AdS black hole solutions of Lovelock gravity. We explore the thermodynamic stability of such solutions by the ordinary method of calculating the specific heat of the black holes and investigating its divergences which signal second order phase transitions between black hole states. We then utilize the methods of thermodynamic geometry of black hole spacetimes in order to explain the origin of these points of divergence. We calculate the curvature scalar corresponding to a Legendre-invariant thermodynamic m…
Bekenstein-Hawking formalism of black hole thermodynamics should be modified to incorporate quantum gravitational effects. Generalized Uncertainty Principle(GUP) provides a suitable framework to perform such modifications. In this paper, we consider a general form of GUP to find black hole thermodynamics in a model universe with large extra dimensions. We will show that black holes radiate mainly in the four-dimensional brane. Existence of black holes remnants as a possible candidate for dark matter is discussed.
In the present work we study (i) charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) black hole in EGB gravity with Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
In this paper, we investigate the phantom energy accretion onto 3D black hole formulated in Einstein-Power-Maxwell theory. We have presented the conditions for critical accretion of phantom energy onto black hole. Further, we discuss the thermodynamics of phantom energy accreting onto black hole and found that first law of thermodynamics is easily satisfied while second law and generalized second law of thermodynamics remain invalid and conditionally valid, respectively. The results for BTZ black hole can be recovered by taking Maxwellian contribution equal to zero.
In this work, we obtain the thermodynamic geometry of the extended black hole solution under f(R) gravity. This is the foundation of our work. We also obtain the exact form of the f(R) model for some solutions. In the thermodynamic analysis, we calculate the thermodynamic quantities such as temperature and entropy of these solutions and compare them with the corresponding BTZ black holes. After that, we study the Ruppeiner geometry, such as the f(R)-gravity (extended black hole solution) of the BTZ black hole, and analyze the thermodynamic comparison of the Ruppeiner geometry with the van der …
In this article we study the thermodynamics of a general non-extremal rotating black hole in minimal five-dimensional gauged supergravity. We analyse the entropy-temperature diagram and the free energy. Additionally we consider the thermodynamic stability by calculating the specific heat, the isothermal moment of inertia tensor and the adiabatic compressibility.
We present an investigation on thermodynamics of two different types of black holes viz. Kiselev black hole (asymptotically flat) and Taub-NUT (non-asymptotically flat) black hole. We compute the thermodynamic variables like black hole's Hawking temperature, entropy at the black hole's event horizon. Further we derive the heat capacity and examine it to study the thermal stability of the black holes. We also calculate the rate of emission assuming the black holes radiate energy in terms of photons by tunneling. We represent all the parameters including the rate of emission of the black holes g…
We study the properties of the space of thermodynamic equilibrium states of the Bañados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a $2-$dimensional thermodynamic metric whose curvature is non-vanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the…
Four classical laws of black hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Hawking's relation $ S=A/4 $ is exactly recovered.
We study the thermodynamic behavior of static and spherically symmetric hairy black holes in massive gravity. In this case, the black hole is surrounded in a spherical cavity with a fixed temperature on the surface. It is observed that these black holes have a phase transition similar to the liquid-gas phase transition of a Van der Waals fluid. Also, by treating the cosmological constant $Λ$ as a thermodynamic pressure $P$, we study the thermodynamic behavior of charged anti-de Sitter black holes in an ensemble with a pressure of $P$ and an electric potential $Φ$ as the natural variables. A se…
Both the canonical and microcanonical ensembles are utilized to study the thermodynamic and evaporation properties of a closed black cosmic string whose spacetime is asymptotically anti deSitter. There are similarities and differences to the Schwarzschild-anti deSitter and 2+1 BTZ black hole solutions. It is found that there exist regimes of black string/thermal radiation equilibrium as well as stable remnant regimes. The relevance to black hole evaporation is discussed.
By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and weak cosmic censorship conjecture (WCCC) with two types of boundary conditions, i.e., the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in the asymptotically at space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and nearextremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change …
Thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, equations of state and thermodynamic response functions are explicitly given and the effect of noncommutativity and quantum correction is discussed. It is shown that the well known divergence exhibited in specific heat is not removed by any of these corrections. However, regions of thermodynamic stability are affected by noncommutativity, increasing the available states for which some thermodynamic stability conditions are satisfi…
We investigate the area spectrum of Kehagias-Sfetsos black hole in Hořava-Lifshitz gravity via modified adiabatic invariant $I=\oint p_i d q_i$ and Bohr-Sommerfeld quantization rule. We find that the area spectrum is equally spaced with a spacing of $ ΔA=4 πl_p ^2$. We have also studied the thermodynamic behavior of KS black hole by deriving different thermodynamic quantities.
Based on a recent proposal for the volume inside a black hole, we calculate the entropy associated with this volume and show that such entropy is proportional to the surface area of the black hole. Together with the consideration of black hole radiation, we find that the thermodynamics associated with the entropy is likely to be caused by the vacuum polarization near the horizon.
In this paper, we study the thermodynamical properties of the (2+1)dimensional black hole with a Coulomb-like electric field and the differential form of the first law of thermodynamics is derived considering a virtual displacement of its event horizon. This approach shows that it is possible to give a thermodynamical interpretation to the field equations near the horizon. The Lambda=0 solution is studied and its interesting thermodynamical properties are commented.
A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner-Nordstrom and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr-Newman case's 3 by 3 thermodynamical state space metric.
We study the thermodynamic properties of black hole horizons in Einstein Gauss Bonnet gravity. We derive the thermodynamic products of characteristic parameters to mark which are global. We further interpret the stability of the black holes by computing the specific heat for both horizons. Stable and unstable phases of horizons are pointed out. The phase transitions with respect to the charge in nature of specific heat are also observed. All these calculation might be helpful to understand the microscopic nature of such black holes.
We show that all thermodynamic quantities of the Einstein-Born-Infeld black holes in three dimensions can be obtained from the dilaton and its potential of two dimensional dilaton gravity through the dimensional reduction. These are all between non-rotating uncharged BTZ black hole (NBTZ) and charged BTZ black hole (CBTZ).
In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to (2+1) dimensional charged BTZ black holes and charged de Sitter space.
We present an approach to the four laws of black hole thermodynamics by utilizing the thermodynamics of quantum coherence. Firstly, Hawking effect is attributed to the decoherence of the two-mode squeezed state in a black hole spacetime. Then use is made of the relative entropy between undecohered and decohered squeezed states whose monotonicity gives the zeroth and the second law, while the first law can be obtained either by the vanishing of the first derivative of relative entropy or by studying the effective thermal model generated by the modular Hamiltonian. Futhermore, information-theore…
We present a new class of the black hole solutions of Einstein-Maxwell-Yang-Mills theory. These solutions have both U(1) charge and Yang-Mills hair. We also investigate the thermodynamic properties.
We study the black hole thermodynamics and obtain the correction terms for temperature, entropy, and heat capacity of the Schwarzschild black hole, resulting from the commutation relations in the framework of {\it Modified Generalized Uncertainty Principle} suggested by {\it Doubly Special Relativity}.
The thermodynamical properties of the Reissner-Nordström-anti-de Sitter black hole in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow us to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and charge. The stability conditions imply that there are thermodynamically stable black hole solutions, under certain conditions. Instantons with negative heat capacity are also found.
We investigate thermodynamics for a magnetically charged regular black hole (MCRBH), which comes from the action of general relativity and nonlinear electromagnetics, comparing with the Reissner-Norström (RN) black hole in both four and two dimensions after dimensional reduction. We find that there is no thermodynamic difference between the regular and RN black holes for a fixed charge $Q$ in both dimensions. This means that the condition for either singularity or regularity at the origin of coordinate does not affect the thermodynamics of black hole. Furthermore, we describe the near-horizon …
Schwarzschild black holes in a de Sitter background were studied in terms of their thermodynamics based on the Rényi statistics. This led to thermodynamically stable black hole configurations for some certain range of black hole radii; namely within this range the corresponding black holes have positive heat capacity. Moreover, for a certain background temperature there can exist at most three configurations of black hole; one among which is thermodynamically stable. These configurations were investigated in terms of their free energies, resulting in the moderate-sized stable black hole config…
We prove that the thermodynamic properties of a Schwarzschild black hole are unaffected by an external magnetic field passing through it. Apart from the background substraction prescription, this result is obtained also by using a counterterm method.
In this review we summarize, expand, and set in context recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. We specifically consider the thermodynamics of higher-dimensional rotating asymptotically flat and AdS black holes and black rings in a canonical (fixed angular momentum) ensemble. We plot the associated thermodynamic potential-the Gibbs free energy-and study its behaviour to uncover possible thermodynamic phase transitions in th…
When the cosmological constant, $Λ$, is interpreted as a thermodynamic variable in the study of black hole thermodynamics a very rich structure emerges. It is natural to interpret $Λ$ as a pressure and define the thermodynamically conjugate variable to be the thermodynamic volume of the black hole (which need not bear any relation to the geometric volume). Recent progress in this new direction for black hole thermodynamics is reviewed.
I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to (i) the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; (ii) the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; (iii) the central role of Hawking radiation in permitting black holes to be in thermal contact …
