Extended Phase Space Thermodynamics Research Articles

Extended phase space thermodynamics of magnetized black holes with nonlinear electrodynamics

Einstein’s gravity in AdS space coupled to nonlinear electrodynamics (NED) with two parameters is studied. We investigate magnetically charged black holes. The metric and mass functions and their asymptotic are obtained showing that black holes may have one or two horizons. Thermodynamics in extended phase space was studied and it was proven that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and the vacuum polarization conjugated to coupling (NED parameter), are computed and depicted. We calculate the Gibbs free energy and heat capacity.

Extended phase space thermodynamics of Bardeen–Letelier black holes in 4D Einstein–Gauss–Bonnet gravity

Extended phase space thermodynamics of Bardeen–Letelier black holes in 4D Einstein–Gauss–Bonnet gravity

Thermodynamic topology of black holes from bulk-boundary, extended, and restricted phase space perspectives

In this article, we investigate the thermodynamic topology of some black holes, namely AdS Reissner Nordstrom (R–N), AdS Einstein–Gauss–Bonnet (EGB), and AdS Einstein-power-Yang–Mills (EPYM), from different frameworks: bulk-boundary (BB) and restricted phase space (RPS). Using the generalized off-shell Helmholtz free energy method, we calculate the thermodynamic topology of the selected black holes in each space separately and determine their topological classifications. We show that the addition of GB terms, dimensions, and other factors do not affect the topological classes of black holes in both spaces. The calculations and plots indicate that the AdS R–N and AdS EGB black holes show similar behavior and their topological numbers sets in both spaces, i.e., BB and RPS, are similar and equal to (W=+1). However, AdS EPYM black holes show an interesting behavior. In addition to BBT and RPS, we also consider the extended phase space thermodynamics (EPST) and evaluate the thermodynamic topology for AdS EPYM black hole. The changing (r−τ) in both spaces shows similar behavior. Also, the topological number and the total topological numbers for this black hole in the BB, RPS and EPS thermodynamics are completely same, i,e., (ωBBT=ωRPS=ωEPST=+1,−1) or WBBT=WRPS=WEPST=0. An important point is that the Einstein–Yang–Mills black hole has thermodynamic topology equivalence in three spaces. The present result may be due to the non-linear YM charge parameter and the difference between the gauge and gravity corrections in the above black holes.

Extended phase space thermodynamics for hairy black holes

Extended phase space thermodynamics for hairy black holes

Magnetic black holes within Einstein–AdS gravity coupled to nonlinear electrodynamics, extended phase space thermodynamics and Joule–Thomson expansion

Einstein’s gravity in Anti-de Sitter space coupled to nonlinear electrodynamics is studied. We analyse the metric, mass functions, and corrections to the Reissner–Nordström solution. Magnetic black holes thermodynamics in extended phase space is investigated. We formulate the first law of black hole thermodynamics showing that the generalized Smarr relation holds. The black hole stability is studied by evaluating the Gibbs free energy and heat capacity. To study the cooling and heating phase transitions of black holes, we consider the Joule–Thomson isenthalpic expansion. The Joule–Thomson coefficient and the inversion temperature are calculated.

Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond

In the extended phase space approach, one can define thermodynamic pressure and volume that gives rise to the van der Waals type phase transition for black holes. For Einstein's GR, the expressions of these quantities are unanimously accepted. Of late, the van der Waals phase transition in black holes has been found in modified theories of gravity as well, such as the $f(R)$ gravity and the scalar-tensor gravity. However, in the case of these modified theories of gravity, the expression of pressure (and, hence, volume) is not uniquely determined. In addition, for these modified theories, the extended phase space thermodynamics has not been studied extensively, especially in a covariant way. Since both the scalar-tensor and the $f(R)$ gravity can be discussed in the two conformally connected frames (the Jordan and the Einstein frame respectively), the arbitrariness in the expression of pressure, will act upon the equivalence of the thermodynamic parameters in the two frames. We highlight these issues in the paper. Before that, in Einstein's gravity (GR), we obtain a general expression of the equilibrium state version of first law and the Smarr-like formula from the Einstein's equation for a general static and spherically symmetric (SSS) metric. Here we directly obtain the first law as well as the Smarr-like formula in GR in terms of the parameters present in the metric (such as mass, charge \textit{etc.}). This study also shows how the extended phase space is formulated (by considering the cosmological constant as variable) and, also shows why the cosmological constant plays the role of thermodynamic pressure in GR in extended phase space. Moreover, obtaining the Smarr formula from the Einstein's equation for the SSS metric suggests that this dynamical equation encodes more information on BH thermodynamics than what has been anticipated before.

Extended phase space thermodynamics of black hole with non-linear electrodynamic field

This paper deals with the thermodynamical properties of the black hole formulated in Einstein's theory of relativity associated with a nonlinear electromagnetic field. The transition of the black hole is analyzed using the mass, electric charge, coupling constant, and cosmological constant. We examine the thermodynamical aspects of exact black hole solutions to compute the black hole mass, temperature, entropy, Gibbs free energy, specific heat, and critical exponents in the phase space. Further, we study the stability of the black hole solution using the specific heat and Gibbs free energy. We examine the first and second phase changes and show a P-V criticality, which is similar to the van der Waals phase change. We also examine the equation of the state and the critical exponents.

Magnetic black holes in AdS space with nonlinear electrodynamics, extended phase space thermodynamics and Joule–Thomson expansion

This paper studies thermodynamics of magnetically charged black holes in Anti-de Sitter space in an extended phase space. The cosmological constant is considered as a pressure and the black hole mass is treated as the chemical enthalpy. The black hole thermodynamics is similar to the Van der Walls liquid–gas thermodynamics. Quantities conjugated to the nonlinear electrodynamics parameter and a magnetic charge are obtained. The first law of thermodynamics and the generalized Smarr relation take place. We investigate critical behavior of black holes and Joule–Thomson expansion. The Gibbs free energy, the Joule–Thomson coefficient and the inversion temperature are calculated.

Extended phase space thermodynamics for dyonic black holes with a power Maxwell field

In this paper, we investigate the thermodynamics of dyonic black holes with the presence of power Maxwell electromagnetic field in the extended phase space, which regards the cosmological constant $\mathrm{\ensuremath{\Lambda}}$ as a thermodynamic variable. For a generic power Maxwell black hole with the electric charge and magnetic charge, the equation of state is given as the function of rescaled temperature $\stackrel{\texttildelow{}}{T}$ in terms of other rescaled variables ${\stackrel{\texttildelow{}}{r}}_{+}$, $\stackrel{\texttildelow{}}{q}$, and $\stackrel{\texttildelow{}}{h}$, where ${r}_{+}$ is the horizon radius, $q$ is the electric charge, and $h$ is the magnetic parameter. For some values of $\stackrel{\texttildelow{}}{q}$ and $\stackrel{\texttildelow{}}{h}$, the phase structure of the black hole is uniquely determined. Moreover, the peculiarity of multiple temperature with some parameter configurations results in complex phase structures. Focusing on the power Maxwell Lagrangian with $\mathcal{L}(s)={s}^{2}$, we obtain the corresponding phase diagrams in the $\stackrel{\texttildelow{}}{h}\text{\ensuremath{-}}\stackrel{\texttildelow{}}{q}$ plane where the critical line extends to $\stackrel{\texttildelow{}}{h}=+\ensuremath{\infty}$. Then, we analyze the black holes' phase structure and critical behavior and display phase transition curves with different $\stackrel{\texttildelow{}}{h}$ in the $\stackrel{\texttildelow{}}{q}\text{\ensuremath{-}}\stackrel{\texttildelow{}}{T}$ plane. We also examine thermal stabilities of these black holes.

Nonlinearly charged AdS black holes, extended phase space thermodynamics and Joule–Thomson expansion

We study thermodynamics and phase transitions of magnetically charged by nonlinear electrodynamics (NED) Anti-de Sitter (AdS) black holes in an extended phase space. The cosmological constant is treated as a thermodynamic pressure whereas the black hole mass is considered such as the chemical enthalpy. The horizon thermodynamics of black holes shows an analogy with the Van der Walls liquid–gas system. We define a quantities which are conjugated to the parameter of NED and a magnetic charge. It is shown that the first law of thermodynamics and the generalized Smarr relation hold. The critical exponents are the same as in the Van der Waals system. The Joule–Thomson adiabatic expansion of NED-AdS black holes is investigated because of thermodynamic behavior of black holes. The Joule–Thomson coefficient, the inversion and isenthalpic curves are discussed. The minimum of inversion temperature and the corresponding event horizon radius are obtained.

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.

Thermodynamic stability and P\u2013V criticality of nonsingular-AdS black holes endowed with clouds of strings

We investigate the extended phase space thermodynamics of nonsingular-AdS black holes minimally coupled to clouds of strings in which we consider the cosmological constant (Lambda ) as the pressure (P) of the black holes and its conjugate variable thermodynamical volume (V) of the black holes. Owing to the background clouds of strings parameter (a), we analyse the Hawking temperature, entropy and specific heat on horizon radius for fixed-parameter k. We find that the strings clouds background does not alter small/large black hole (SBH/LBH) phase transition but occurs at a larger horizon radius, and two second-order phase transitions occur at a smaller horizon radius. Indeed, the G–T plots exhibit a swallowtail below the critical pressure, implying that the first-order phase transition is analogous to the liquid–gas phase transition at a lower temperature and lower critical pressure. To further examine the analogy between nonsingular-AdS black holes and a liquid–gas system, we derive the exact critical points and probe the effects of a cloud of strings on P-V criticality to find that the isotherms undergo liquid–gas like phase transition for {tilde{T}},<,{tilde{T}}_c at lower {tilde{T}}_c. We have also calculated the critical exponents identical with Van der Walls fluid, i.e., same as those obtained before for arbitrary other AdS black holes, which implies that the background clouds of strings do not change the critical exponents.

Central charge criticality of charged AdS black hole surrounded by different fluids

We analyze the extended phase space thermodynamics of Kiselev black hole introducing a central charge and allowing the gravitational constant to vary. We also discuss the relation between the chemical potential and the size of the black hole, besides the new description of phase transitions. We obtain as a conclusion that the universality of the central charge does not remain valid in general.

Phase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source

In this work we consider black hole solutions to Einstein’s theory coupled to a nonlinear power-law electromagnetic field with a fixed exponent value. We study the extended phase space thermodynamics in canonical and grand canonical ensembles, where the varying cosmological constant plays the role of an effective thermodynamic pressure. We examine thermodynamical phase transitions in such black holes and find that both first- and second-order phase transitions can occur in the canonical ensemble while, for the grand canonical ensemble, Hawking–Page and second-order phase transitions are allowed.

Joule-Thomson expansion of AdS black holes in Einstein Power-Yang-mills gravity

In this paper we study Joule-Thomson expansion of non-linearly charged AdS black holes in Einstein-power-Yang-Mills (EPYM) gravity in D dimensions. Within the framework of extended phase space thermodynamics we identify the cosmological constant as thermodynamic pressure and the black hole mass with the enthalpy to derive the Joule- Thomson coefficient μ. Furthermore we have presented equations for inversion curves and the exact expression for the minimum inversion temperature. We also have calculated the ratio between the minimum of inversion temperature and the critical temperature T c and obtained the analytic expression for the ratio that depends explicitly on the non- linearity parameter q and dimension D. We consider the isenthalpic curves in the T − P plane for different values of the fixed black hole mass and obtain heating and cooling region. Finally we have dealt with two limiting masses which characterizes the process of Joule-Thomson expansion in the EPYM black holes.

Instability of regular electric black hole

A new spherically symmetric exact solution of Einstein gravity in the presence of a nonlinear electromagnetic field is introduced. It is shown that such a solution can be interpreted as an electrically charged regular black hole that behaves like Reissner−Nordström metric, asymptotically. An extension of the solution in the presence of cosmological constant is presented and thermodynamic properties of the solution are studied in the extended phase space thermodynamics. Then, thermal stability and possible phase transition are investigated and the van der Waals like behavior is observed. Finally, the relation between the photon sphere with a thermodynamic phase transition is studied.

Extended phase space thermodynamics for third-order Lovelock black holes with nonmaximally symmetric horizons

We study thermodynamics and critical behaviors of higher-dimensional Lovelock black holes with non-maximally symmetric horizons in the canonical ensemble of extended phase space. The effects from non-constancy of the horizon of the black hole via appearing two chargelike parameters in thermodynamic quantities of third-order Lovelock black holes are investigated. We find that Ricci flat black holes with nonconstant curvature horizon show critical behavior. This is an interesting feature that is not seen for any kind of black hole in Einstein or Lovelock gravity in the literature. We examine how various interesting thermodynamic phenomena such as standard first-order small-large black hole phase transition, a reentrant phase transition, or zeroth order phase transition happens for Ricci flat, spherical, or hyperbolic black holes with nonconstant curvature horizon depending on the values of Lovelock coefficient and chargelike parameters. While for a spherical black hole of third order Lovelock gravity with constant curvature horizon phase transition is observed only for $7\leq d \leq11$, for our solution criticality and phase transition exist in every dimension. With a proper choice of the free parameters, a large-small-large black hole phase transition occurs. This process is accompanied by a finite jump of the Gibbs free energy referred to as a zeroth-order phase transition. For the case $\kappa=-1$ a novel behavior is found for which three critical points could exist.

Charged black hole solutions with Toroidal horizons in f(R)-gravity surrounded by quintessence and cloud of strings: Effective potential barrier, quasinormal modes

We construct a new class of [Formula: see text]-dimensional black hole solutions with Toroidal horizons in [Formula: see text] gravity framework which is surrounded by quintessence and string cloud configuration, whose asymptotic structures are determined by the quintessential state parameter [Formula: see text] and dimension’s parameter [Formula: see text]. We point out that the asymptotic behavior of the obtained solutions is neither asymptotically flat nor (A)dS when we have [Formula: see text] and [Formula: see text]. Regarding the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we investigate the critical behavior of our black hole solutions. In [Formula: see text] and [Formula: see text], the P–V diagrams are more complex than that of the standard Van der Waals. These diagrams behave like the Born–Infeld-AdS P–V diagrams. When [Formula: see text] and [Formula: see text], the P–V diagrams behave like the standard Van der Waals system (In this work [S. Gunasekaran, D. Kubiznaak and R. B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012).] [S. Gunasekaran, D. Kubiznaak and R.B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012)], the authors believe that the BTZ black holes, contrary to the higher-dimensional case, do not show any critical behavior. In this work, we have showed that the three-dimensional (3D) black holes can also have critical behavior and coincide with those of the Van der Waals system). Besides, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. We figure out the effect of the coupling constant [Formula: see text], the string parameter b, and the quintessential state parameter [Formula: see text] on the height of the potential barrier and the other thermodynamical quantities like temperature and heat capacity. Then, we study the quasinormal modes (QNMs) of 3D black holes in the [Formula: see text] context. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation’s decay in corresponding diagrams when the string parameter b changes.

Extended phase space thermodynamics of Bardeen black hole in massive gravity

We present an exact solution of Bardeen AdS black hole in massive gravity theory by taking into account the massive gravity parameter m and study its thermodynamic properties such as temperature, entropy and heat capacity at constant pressure. We also study the critical behaviour of Bardeen AdS massive black holes by taking the cosmological constant $$\Lambda $$ as the thermodynamic pressure, and it is shown that thermodynamic volume is independent of the massive gravity parameter m. In addition to these, we investigate the dependence of critical parameters on the massive gravity parameter (m) and magnetic monopole charge (e). It is observed that the critical exponents (critical temperature and critical pressure) increase with massive gravity parameter but decrease in the presence of magnetic monopole charge. Also the numerical value of ratio $$P_\mathrm{c}r_\mathrm{c}/T_\mathrm{c}$$ increases with increase in the values of the parameters m and e.

Extended phase space thermodynamics for black holes in a cavity

In this paper, we extend the phase space of black holes enclosed by a spherical cavity of radius rB to include V=4pi {r}_B^3/3 as a thermodynamic volume. The thermodynamic behavior of Schwarzschild and Reissner-Nordstrom (RN) black holes is then investigated in the extended phase space. In a canonical ensemble at constant pressure, we find that the aforementioned thermodynamic behavior is remarkably similar to that of the anti-de Sitter (AdS) counterparts with the cosmological constant being interpreted as a pressure. Specifically, a first-order Hawking-Page-like phase transition occurs for a Schwarzschild black hole in a cavity. The phase structure of a RN black hole in a cavity shows a strong resemblance to that of the van der Waals fluid. We also display that the Smarr relation has the same expression in both AdS and cavity cases. Our results may provide a new perspective for the extended thermodynamics of AdS black holes by analogy with black holes in a cavity.