Law Of Black Hole Thermodynamics Research Articles

AdS Black Holes in the Framework of Nonlinear Electrodynamics, Thermodynamics, and Joule–Thomson Expansion

The thermodynamics and phase transitions of magnetic Anti-de Sitter black holes were studied. We considered extended-phase-space thermodynamics, with the cosmological constant being a thermodynamic pressure and the black hole mass being treated as a chemical enthalpy. The extended-phase-space thermodynamics of black holes mimic the behavior of a Van der Waals liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It was demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation hold. The Joule–Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of the inversion temperature are found.

Hawking evaporation, shadow images, and thermodynamics of black holes through deflection angle

We study the Hawking evaporation process of the exact black hole with nonlinear electrodynamics for positive and negative coupling constant zeta . We provide a new perspective to study the thermodynamics of exact black hole through deflection angle formalism. We also evaluate the shadow images in the presence of deflection images for this black hole. Moreover, we consider the Gibbs energy optical dependence to investigate the Hawking-Page transition. We observe that evaporation rate depends upon zeta and black hole evaporates more quickly for positive zeta as compared to negative zeta . For the case zeta =-1, the black hole’s lifetime become infinite, which makes the black hole a remnant and the third law of black hole thermodynamics holds in this scenario. We show that the thermal variations in the deflection angle can be used to determine the stable and unstable phases of the black hole. Our findings show that large and small phase transitions of black hole occur at a specific value of the deflection angle.

Hairy black holes in general minimal massive gravity

In this work, we investigate the near horizon and asymptotic symmetries of static and rotating hairy-AdS black hole in the framework of general minimal massive gravity. We obtain energy, angular momentum and entropy of the solutions. Then we show that our results for these quantities are consistent with the first law of black hole thermodynamics. By considering the near horizon geometry of black hole, we find near horizon conserved charges and their algebra. By writing the algebra of conserved charges in terms of Fourier modes we have obtained the conserved charges in terms of zero modes.

Rational non-linear electrodynamics of AdS black holes and extended phase space thermodynamics

The critical behaviour of magnetically charged AdS black holes based on rational non-linear electrodynamics (RNED) in an extended phase space is investigated herein. The cosmological constant is considered as thermodynamic pressure, and the black hole mass is identified with the chemical enthalpy. An analogy with the van der Walls liquid–gas system is found, and the critical exponents coincide with those of the van der Waals system. The thermodynamics of RNED-AdS black holes and phase transitions are studied, and new thermodynamic quantities conjugated to the non-linear parameter of RNED and magnetic charge are defined. The consistency of the first law of black hole thermodynamics and the Smarr formula is demonstrated.

Restricted phase space thermodynamics for AdS black holes via holography

A new formalism for thermodynamics of AdS black holes called the restricted phase space thermodynamics (RPST) is proposed. The construction is based on top of Visser’s holographic thermodynamics, but with the AdS radius fixed as a constant. Thus the RPST is free of the (P, V) variables but inherits the central charge and chemical potential as a new pair of conjugate thermodynamic variables. In this formalism, the Euler relation and the Gibbs–Duhem equation hold simultaneously with the first law of black hole thermodynamics, which guarantee the appropriate homogeneous behaviors for the black hole mass and the intensive variables. The formalism is checked in detail in the example case of four-dimensional Reissner–Nordström anti-de Sitter black hole in Einstein–Maxwell theory, in which some interesting thermodynamic behaviors are revealed.

(2+1)-dimensional black holes of Einstein\u2019s theory with Born\u2013Infeld type electrodynamic sources

A new family of (2+1)-dimensional black holes are investigated in the background of Born–Infeld type theories coupled to a Riemannian curved spacetime. We know that both the scale and dual invariances are violated for these nonlinear electromagnetic theories. In this set-up, first we consider a pure magnetic source in a model of exponential electrodynamics and find a magnetically charged (2+1)-dimensional black hole solution in terms of magnetic charge q and nonlinearity parameter beta . In the second case we consider a pure electric source of gravity in the framework of arcsin electrodynamics and derive the associated (2+1)-dimensional black hole solution in terms of electric charge Q and the parameter beta . The asymptotic behaviour of the solutions at infinity as well as at rrightarrow 0 in both the frameworks is discussed. The asymptotic expressions of curvature invariants in the case of exponential electrodynamics shows that there exists a finite value of curvature at the origin, while in arcsin electrodynamics, the corresponding asymptotic behaviour shows that there is a true curvature singularity at the centre of the charged object. Furthermore, thermodynamics of the resulting charged black holes within the context of both the models is studied. It is shown that the thermodynamic quantities corresponding to these objects satisfy the first law of black hole thermodynamics.

The first law of black hole thermodynamics for Taub–NUT spacetime

This paper focuses on the new approach to the nature of a nut parameter [Formula: see text], usually treated as a dual charge to the mass. Instead of thinking about it as a gravitational analog of the magnetic monopole, we will show that the Taub–NUT spacetime conceals a peculiar rotation coming from the Misner strings depending on the nut value. Besides reconciling several confusing results present in the literature, this allows us to establish more the less a consistent description of the black hole thermodynamics for the Lorentzian Taub–NUT spacetime with essential contribution from the Misner strings to the angular momentum and total entropy.

Generalized proof of the linearized second law in general quadric corrected Einstein-Maxwell gravity

Although the entropy of black holes in any diffeomorphism invariant theory of gravity can be expressed as the Wald entropy, the issue of whether the entropy always obeys the second law of black hole thermodynamics remains open. Since the nonminimal coupling interaction between gravity and the electromagnetic field in the general quadric corrected Einstein-Maxwell gravity can sufficiently influence the expression of the Wald entropy, we check whether the Wald entropy of black holes in the quadric corrected gravity still satisfies the second law. A quasistationary accreting process of black holes is first considered, which describes that black holes are perturbed by matter fields and eventually settle down to a stationary state. Two assumptions that the matter fields should obey the null energy condition and that a regular bifurcation surface exists on the background spacetime are further proposed. According to the two assumptions and the Raychaudhuri equation, we demonstrate that the Wald entropy monotonically increases along the future event horizon under the linear order approximation of the perturbation. This result indicates that the Wald entropy of black holes in the quadric corrected gravity strictly obeys the linearized second law of thermodynamics.

Solid-liquid phase transition and heat engine in an asymptotically flat Schwarzschild black hole via the Rényi extended phase space approach

Recently, it has been found that, with the R\'enyi statistics, the asymptotically flat Schwarzschild black hole can be in thermal equilibrium with infinite heat reservoir at a fixed temperature when its event horizon radius is larger than the characteristic length scale ${L}_{\ensuremath{\lambda}}=1/\sqrt{\ensuremath{\pi}\ensuremath{\lambda}}$, where $\ensuremath{\lambda}$ is the nonextensivity parameter. In the R\'enyi extended phase space with the $PdV$ work term, an off shell free energy in the canonical ensemble with the thermodynamic volume as an order parameter is considered to identify a first-order Hawking-Page (HP) phase transition as a solid-liquid phase transition. It has the latent heat of fusion from solid (corresponding to thermal radiation) to liquid (corresponding to black hole) in the form of $\ensuremath{\sim}1/\sqrt{\ensuremath{\lambda}}$; this is evident in the absence of the HP phase transition in the case of an asymptotically flat Schwarzschild black hole from the Gibbs-Boltzmann statistics ($\ensuremath{\lambda}=0$). Moreover, we investigate the generalized second law of black hole thermodynamics (GSL) in R\'enyi statistics by considering the black hole as a working substance in a heat engine. Interestingly, an efficiency $\ensuremath{\eta}$ of the black hole in a Carnot cycle takes the form ${\ensuremath{\eta}}_{c}=1\ensuremath{-}{T}_{\mathrm{C}}/{T}_{\mathrm{H}}$. This confirms the validity of the GSL in the R\'enyi extended phase space.

First law of black hole in the gravitational electromagnetic system

After considering the quantum corrections of Einstein-Maxwell theory, the effective theory will contain some higher-curvature terms and nonminimally coupled electromagnetic fields. In this paper, we study the first law of black holes in the gravitational electromagnetic system with the Lagrangian ℒ(gab, Rabcd, Fab). Firstly, we calculate the Noether charge and the variational identity in this theory, and then generically derive the first law of thermodynamics for an asymptotically flat stationary-axisymmetric symmetric black hole without the requirement that the electromagnetic field is smooth on the bifurcation surface. Our results indicate that the first law of black hole thermodynamics might be valid for the Einstein-Maxwell theory with some quantum corrections in the effective region.

Thermodynamics and weak cosmic censorship conjecture of the high dimensional hairy AdS spacetime

In order to further verify the weak cosmic censorship conjecture in high-dimensional hairy space-time, we discuss the thermodynamics and the weak cosmic censorship conjecture from a five-dimensional hairy AdS black hole. With the absorption fermions by hairy AdS black holes, the energy-momentum relationship at the horizon is obtained via Dirac equations. Based on this energy-momentum relationship, we derive entropy variation and the change of the function that determines the minimum value of the event horizon. It turns out the first and second laws of black hole thermodynamics and the weak cosmic censorship conjecture are valid in high-dimensional hairy space-time.

Holographic bound on area of a compact binary merger remnant

Using concomitantly the generalized second law of black hole thermodynamics and the holographic Bekenstein entropy bound embellished by loop quantum gravity corrections to quantum black hole entropy, we show that the boundary cross sectional area of the postmerger remnant formed from the compact binary merger in gravitational wave detection experiments like GW150914 et seq., by the LIGO-VIRGO collaboration, is bounded from below. This lower bound is more general than the bound obtained from application of Hawking's classical area theorem for black holes, since it does not depend on whether the inspiralling compact binary pair or the postmerger remnant consists of black holes or other exotic compact objects. The derivation of the bound entails an estimate of the entropy of the gravitational waves emitted during the binary merger, which adapts to gravitational waves an extant formalism proposed originally for particle ensembles. The results for the minimal cross sectional area of the merger remnant due to binary compact mergers observed recently by the LIGO-VIRGO collaboration are discussed. While accurate measurement of the mass of the remnant for the binary neutron star merger GW170817 remains a challenge, we provide a proof of principle that for binary neutron star mergers our lower bound on the cross sectional area of the remnant provides an alternative approach to probe the validity of neutron star equations of state, independent of the tidal deformabilities of the components.

Counterterm method and thermodynamics of hairy black holes in a vector-tensor theory with Abelian gauge symmetry breaking

For a type of nonminimally coupled vector-tensor theories with Abelian gauge symmetry breaking in four-dimensional spacetime and correspondingly asymptotic non-AdS black hole solutions including a cosmological constant, we construct the appropriate boundary terms and derive the associated junction condition. In order to remove the divergences in the stress tensor which is localized on the spacetime boundary, we also involve the suitable surface counterterms into the total action. Using the counterterm method, we calculate the black hole mass. An implicit relation between the black hole carge $Q$ and other parameters is implied by combining the expression of the black hole mass with the first law of black hole thermodynamics. With this implicit relation, we can prove the inequality $Q\ensuremath{\le}M$ which is a general bound for most of charged black holes. Besides, the phase structure of black holes is also investigated in the grand canonical ensemble.

First law of black hole thermodynamics and Smarr formula with a cosmological constant

The first law of black hole thermodynamics in the presence of a cosmological constant $\mathrm{\ensuremath{\Lambda}}$ can be generalized by introducing a term containing the variation $\ensuremath{\delta}\mathrm{\ensuremath{\Lambda}}$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge, etc., it has been shown [Classical Quant. Grav. 35, 125012 (2018)] that the new term has the same structure: $\mathrm{\ensuremath{\Lambda}}$ is a conserved charge associated with a gauge symmetry; and its role in the first law is quite similar to an ``electric charge'' rather than to the pressure. Besides, its conjugate chemical potential resembles an ``electric potential'' on the horizon, in contrast with the volume enclosed by horizon. In this work, first we propose and prove the generalized Smarr relation in this new paradigm. Then, we reproduce systematically the ``effective volume'' of a black hole which has been introduced before in the literature as the conjugate of pressure. Our construction removes the ambiguity in the definition of volume. Finally, we apply and investigate this formulation of ``$\mathrm{\ensuremath{\Lambda}}$ as a charge'' on a number of solutions to different models of gravity for different spacetime dimensions. Especially, we investigate the applicability and validity of the analysis for black branes, whose enclosed volume is not well defined in principle.

Stability of remnants of Bardeen regular black holes in presence of thermal fluctuations

In this paper, we discuss remnants of the Bardeen regular black hole motivated by using the concept of thermal fluctuations. First, we derive the equilibrium values of various thermodynamic quantities like entropy, Hawking temperature, pressure, internal energy, Helmholtz free energy and Gibbs free energy in the non-extended phase space. We then discuss geometrothermodynamics (GTD) of Bardeen black hole to study its stability. Next, we estimate the size of black hole remnant in terms of some known parameters of the black hole solution. Motivated by the fact that estimation of size, characteristics and stability of remnants of black holes could further increase our understanding of binary collisions, information loss paradox and dark energy, the black hole remnant, which gives an idea about stable mass left over after evaporation of black hole, is seen to owe its presence due to thermal fluctuations. We see that the thermal fluctuations bring an overall increase in entropy curve. However, in presence of thermal fluctuations, a positive kink, which signifies a maximum increase in the value of entropy, occurs at a certain value of horizon, which is exactly equal to the remnant radius. We observe that the thermal fluctuations, which are characteristics of quantum gravity, lead to stable values of thermodynamic quantities near the remnant radius. In presence of thermal fluctuations, we then derive various corrected thermodynamic potentials and also discuss the validity of first law of black hole thermodynamics for Bardeen black hole.

Black hole in Nielsen-Olesen vortex

In this article, we calculate the classical vortex solution of a spontaneously broken gauge theory interacting with gravity in (2+1)-dimension. We also calculate the conditions for the formation of a (2+1)-dimensional black hole due to magnetic vortex (a Nielsen-Olesen vortex). The semiclassical Hawking temperature for this black hole is calculated, where we see that the temperature of a BTZ black hole increases or decreases without changing the size of the horizon if we insert the magnetic vortex fields in the black hole. Finally, the first law of black hole thermodynamics is described for this particular solution, which shows that the additional work terms from the scalar and gauge fields compensate the change in the temperature relative to its usual value for the BTZ solution.

Can Naked Singularities Exist Without Violating The Laws of Black Hole Thermodynamics?

According to the cosmic censorship conjecture, it is impossible for nature to have a physical singularity without a horizon because if it were to arise in any formalism, for instance as an extremal black hole (Kerr or Reissner-Nordstrom) then the surface gravity κ = 0, which is a strict violation of the third law of black hole thermodynamics. In this paper we explore whether a true singularity can exist without defying this law.

Quantum corrected thermodynamics of nonlinearly charged BTZ black holes in massive gravity’s rainbow

In this paper, we consider three-dimensional massive gravity’s rainbow and obtain black hole solutions in three different cases of Born–Infeld, logarithmic, and exponential theories of nonlinear electrodynamics. We discuss the horizon structure and geometrical properties. Then, we study thermodynamics of these models by considering the first-order quantum correction effects, which appear as a logarithmic term in the black hole entropy. We discuss such effects on the black hole stability and phase transitions. We find that due to the quantum corrections, the second-order phase transition happens in Born–Infeld and logarithmic models. We obtain the modified first law of black hole thermodynamics in the presence of logarithmic corrections.

Lost horizon? – modeling black holes in string theory

The modeling of black holes is an important desideratum for any quantum theory of gravity. Not only is a classical black hole metric sought, but also agreement with the laws of black hole thermodynamics. In this paper, we describe how these goals are obtained in string theory. We review black hole thermodynamics, and then explicate the general stringy derivation of classical spacetimes, the construction of a simple black hole solution, and the derivation of its entropy. With that in hand, we address some important philosophical and conceptual questions: the confirmatory value of the derivation, the bearing of the model on recent discussions of the so-called 'information paradox', and the implications of the model for the nature of space.

Binary black hole system at equilibrium

An exact and analytical solution of four dimensional vacuum General Relativity representing a system of two static black holes at equilibrium is presented. The metric is completely regular outside the event horizons, both from curvature and conical singularities. The balance between the two Schwarzschild sources is granted by an external gravitational field, without the need of extra matter fields besides gravity, nor strings or struts. The geometry of the solution is analysed. The Smarr law, the first and the second law of black hole thermodynamics are discussed.