Thermodynamics of accelerating and rotating black holes

General Relativity and Gravitation, 2013

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge

Gravitation and Cosmology, 2017

We investigate the thermodynamics of Kerr-Newman-Kasuya black hole and the Reissner-Nordström black hole with a global monopole on inner and outer horizons. Products of surface gravities, surface temperatures, Komar energies, electromagnetic potentials, angular velocities, areas, entropies, horizon radii and the irreducible masses at the Cauchy and the event horizons are calculated. It is observed that the product of surface gravities, surface temperature product and product of Komar energies, electromagnetic potentials and angular velocities at horizons are not universal quantities for these black holes. Products of areas and entropies at horizons are independent of masses of black holes. Heat capacity is calculated for the generalized charged rotating black hole and phase transition is observed, under certain conditions on r.

Journal of Physics: Conference Series, 2019

In this paper we calculate the Hawking temperature of a black hole described by the Kerr-Newman metric, starting from the surface gravity, the area of the event horizon and the angular velocity of the black hole. To do this we apply the laws of black hole thermodynamics: we first set the energy conservation through a relationship between the mass M, the charge Q and the angular momentum J, then we implement the Hawking's theorem of areas by setting an upper bound to the energy and we get finally the surface gravity of the black hole. In addition, we study the relationship between the black hole parameters (mass M, angular momentum J, electric charge Q) and the Hawking temperature. 1. Introduction In 1974 Hawking [1,2] predicted that the curvature of space-time at the event horizon of a black hole is sufficient to excite photons from vacuum and cause a continuous flow of them, known as Hawking radiation. The continuous process causes the black hole to lose energy with the consequent decrease of its mass, until after a while and the hole disappears completely. Hawking predicted that this radiation has a well-defined temperature proportional to the superficial gravity in its horizon of events. In 2009 V. Pankovic [3], presents a simplified method for describing and calculating the basic characteristics, dynamics (horizons) and thermodynamics of a Kerr-Newman black hole. His method was based on principles of classical mechanics, electrodynamics, thermodynamics, statistics, non-relativistic quantum mechanics and on the elementary form of the general principle of relativistic equivalence; which represented results already proposed in the theory of quantum gravity. In 2010 F. Belgiorno and his colleagues [4], created an optical analogue of the event horizon of a black hole, the results of which coincide with Stephen Hawking's quantum predictions for radiation emitted by a black hole evaporating. If the result of Franco Belgiorno and his colleagues is confirmed, it would be the first observation of Hawking radiation. This paper presents a simplified method for estimating Hawking temperature and evaporation time of Kerr-Newman black holes. The relationship between the hole parameters (mass M, angular momentum J, electric charge Q) and this time is also studied.

Thermodynamics of extended gravity static spherically symmetric black hole solutions is investigated. The energy issue is discussed making use of the derivation of Clausius relation from equations of motion, evaluating the black hole entropy by the Wald method and computing the related Hawking temperature.

2009

In this letter, we construct a class of (n+1)-dimensional (n ≥ 3) slowly rotating black hole solutions in Maxwell-Brans-Dikce theory with quadratic potential. These solutions can present black holes with inner and outer event horizons, an extreme black hole and a naked singularity and they are neither asymptotically flat nor (anti)-de Sitter. We compute the finite action through the use of the counterterm method and then use the relation between the action and free energy in grand canonical ensemble to obtain the conserved and thermodynamics quantities. We also compute the angular momentum and the gyromagnetic ratio for these type of black holes. Finally we show that these quantities satisfy the first law of thermodynamics. Moreover we will find that the entropy in this case does not obey the area law.

International Letters of Chemistry, Physics and Astronomy, 2015

A simple model was setup to find the mass variation over time for a Schwarzschild black hole. The temperature and entropy of a black hole was obtained from the numerically solved mass variation and the time variations of the black hole thermodynamic parameters were simulated. The mass of a given black hole reduces rapidly. The time taken for a black hole to vanish increases in an increasing rate with the given initial mass of the black hole. The temperature of a black hole drastically increases at the final stage of the black hole evaporation. The colour attributed to that temperature was found to be in the visible region for a significant amount of time. The black hole entropy also drastically reduces with its mass and through Hawking radiation it is added to the rest of the universe.

Journal of High Energy Physics

We revisit the first law of black hole thermodynamics in 4-dimensional theories containing scalar and Abelian vector fields coupled to gravity using Wald’s formalism and a new definition of scalar charge as an integral over a 2-surface which satisfies a Gauss law in the background of stationary black-hole spacetimes. We focus on ungauged supergravity-inspired theories with symmetric sigma models whose symmetries generate electric-magnetic dualities leaving invariant their equations of motion. Our manifestly duality-invariant form of the first law is compatible with the one obtained by of Gibbons, Kallosh and Kol. We also obtain the general expression for the scalar charges of a stationary black hole in terms of the other physical parameters of the solution and the position of the horizon, generalizing the expression obtained by Pacilio for dilaton black holes.

Physical Review D, 2011

We study the thermodynamics and the thermodynamic geometries of charged rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the thermodynamics of these systems within the context of the Weinhold and Ruppeiner thermodynamic geometries and the recently developed formalism of geometrothermodynamics (GTD). Considering the behavior of the heat capacity and the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot describe completely the thermodynamics of these black holes and of their limiting case of vanishing electric charge. In contrast, the Legendre invariance imposed on the metric in GTD allows one to describe the CR-BTZ black holes and their limiting cases in a consistent and invariant manner.

General Relativity and Gravitation, 2022

In this paper, we study thermodynamic features of the charged rotating accelerating black holes in anti-de Sitter spacetime. First, we consider these black holes as the thermodynamic systems and analyze thermal stability/instability through the use of heat capacity in the canonical ensemble. We also investigate the effects of angular momentum, electric charge and string tension on the thermodynamic quantities and stability of the system. Considering the known relation between pressure and the cosmological constant, we extract the critical quantities and discuss how the mentioned parameters affect them. Then, we construct a heat engine by taking into account this black hole as the working substance, and obtain the heat engine efficiency by considering a rectangle heat cycle in the P − V plane. We examine the effects of black hole parameters on the efficiency and analyze their effective roles. Finally, by comparing the engine efficiency with Carnot efficiency, we investigate conditions in order to have a consistent thermodynamic second law.

Physical Review D, 2021

As the interaction between the black holes and highly energetic infalling charged matter receives quantum corrections, the basic laws of black hole mechanics have to be carefully rederived. Using the covariant phase space formalism, we generalize the first law of black hole mechanics, both "equilibrium state" and "physical process" versions, in the presence of nonlinear electrodynamics fields, defined by Lagrangians depending on both quadratic electromagnetic invariants, F ab F ab and F ab ⋆F ab. Derivation of this law demands a specific treatment of the Lagrangian parameters, similar to embedding of the cosmological constant into thermodynamic context. Furthermore, we discuss the validity of energy conditions, several complementing proofs of the zeroth law of black hole electrodynamics and some aspects of the recently generalized Smarr formula, its (non-)linearity and relation to the first law.

2008

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the 5-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner-Nordstr\"om black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner-Nordstr\"om black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincar\'e stability analysis shows no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q<0 parameter range, which enhances the localization of gravity on the brane, is thermodynamically preferred. Finally we constrain for the first time the possible range of the tidal charge from the thermodynamic limit on gravitational radiation efficiency at black hole mergers.

European Physical Journal C, 2011

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the five-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner–Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner–Nordströ m black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincaré stability analysis show no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q

Physics Letters B, 2007

In this paper, we study different cases of the charged rotating BTZ black hole with reference to their horizons. For the existence of these cases conditions on mass, charge and angular momentum of the black hole are obtained. It is also shown that the Einstein field equations for the charged rotating BTZ black hole at the horizon can be expressed as first law of thermodynamics, dE = T dS + ΩdJ + Φdq + P r dA.

1997

We review and correct the classical critical exponents characterizing the transition from negative to positive black hole's heat capacity at high chargeangular momentum. We discuss the stability properties of black holes as a thermodynamic system in equilibrium with a radiation bath (canonical ensamble) by using the Helmholtz free energy potential. We finally analytically extend the analysis to negative mass holes and study its thermodynamical stability behavior.

We continue to explore the consequences of Thermal Relativity Theory to the physics of black holes. The thermal analog of Lorentz transformations in the tangent space of the thermodynamic manifold are studied in connection to the Hawking evaporation of Schwarzschild black holes and one finds that there is no bound to the thermal analog of proper accelerations despite the maximal bound on the thermal analog of velocity given by the Planck temperature. The proper entropic infinitesimal interval corresponding to the Kerr-Newman black hole involves a 3 × 3 non-Hessian metric with diagonal and off-diagonal terms of the form (ds)^2 = g_{ab} (M, Q, J)dZ^a dZ^b , where Z^a = M, Q, J are the mass, charge and angular momentum, respectively. Black holes in asymptotically Anti de Sitter (de Sitter) spacetimes are more subtle to study since the mass turns out to be related to the enthalpy rather that the internal energy. We finalize with some remarks about the thermal-relativistic analog of proper force, the need to extend our analysis of Gibbs-Boltzmann entropy to the case of Reny and Tsallis entropies, and to complexify spacetime.