scholarly journals The thermodynamics of a Kerr–Newman–de Sitter black hole

2003 ◽  
Vol 81 (12) ◽  
pp. 1363-1375 ◽  
Author(s):  
M H Dehghani ◽  
H KhajehAzad
Keyword(s):  
Black Hole ◽  
Stability Analysis ◽  
Hessian Matrix ◽  
Shift Factor ◽  
De Sitter ◽  
Complete Set ◽  
Thermodynamic Variables ◽  
Renormalization Method ◽  
Canonical Ensembles ◽  
Grand Canonical

We compute the conserved quantities of the four-dimensional Kerr–Newman–de Sitter (KNdS) black hole through the use of the counterterm renormalization method, and obtain a generalized Smarr formula for the mass as a function of the entropy, the angular momentum, and the electric charge. The first law of thermodynamics associated to the cosmological horizon of KNdS is also investigated. Using the minimal number of intrinsic boundary counterterms, we consider the quasilocal thermodynamics of an asymptotic de Sitter–Reissner–Nordstrom black hole, and find that the temperature is equal to the product of the surface gravity (divided by 2π) and the Tolman red-shift factor. We also perform a quasilocal stability analysis by computing the determinant of Hessian matrix of the energy with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles and obtain a complete set of phase diagrams. We then turn to the quasilocal thermodynamics of four-dimensional Kerr–Newman–de Sitter black hole for virtually all possible values of the mass, the rotation, and the charge parameters that leave the quasilocal boundary inside the cosmological event horizon, and perform a quasilocal stability analysis of KNdS black hole.PACS Nos.:04.70.Dy, 04.62.+v, 04.60.–m

Thermodynamics of black holes with higher order corrected entropy

2019 ◽  
Vol 97 (7) ◽  
pp. 742-751 ◽  
Author(s):  
M. Umair Shahzad ◽  
Abdul Jawad
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Higher Order ◽  
De Sitter ◽  
Free Energies ◽  
Corrected Entropy ◽  
The Stability ◽  
Canonical Ensembles ◽  
Thermodynamical Behavior ◽  
Correction Terms

For analyzing the thermodynamical behavior of two well-known black holes, such as Reissner–Nordström – anti-de Sitter (RN-AdS) black hole with global monopole and f(R) black hole, we consider the higher order logarithmic corrected entropy. We develop various thermodynamical properties, such as entropy, specific heat, pressure, and Gibbs and Helmhotz free energies for both black holes in the presence of corrected entropy. A versatile study on the stability of black holes is made by using various frameworks, such as the ratio of heat capacities (γ), grand canonical and canonical ensembles, and phase transition in view of higher order logarithmic corrected entropy. It is observed that both black holes exhibit more stability (locally as well as globally) for growing values of cosmological constant and higher order correction terms.

scholarly journals Thermodynamic properties of Bardeen black holes in dRGT massive gravity

2021 ◽  
Author(s):  
R P Singh ◽  
B K Singh ◽  
B R K Gupta ◽  
S Sachan
Keyword(s):  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Black Hole Solution ◽  
Massive Gravity ◽  
Schwarzschild Black Hole ◽  
Regular Black Hole ◽  
Horizon Radius ◽  
Canonical Ensembles ◽  
Grand Canonical

The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is the modification of the Schwarzschild black hole. We present the Bardeen black hole solution in presence of the dRGT massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution interpolates with the Bardeen black hole in the absence of massive gravity parameter and the Schwarzschild black hole in the limit of magnetic charge g=0. We investigate the thermodynamical quantities viz. mass (M), temperature (T), entropy (S) and free energy (F) in terms of horizon radius for both canonical and grand canonical ensembles. We check the local and global stability of the obtained solution by studying the heat capacity and free energy. The heat capacity flips the sign at r = r<sub>c</sub>. The black hole is thermodynamically stable with positive heat capacity C>0 for i.e., globally preferred with negative free energy F < 0. In addition, we also study the phase structure of the obtained solution in both ensembles.

The Free Energy for Rotating and Charged Black Holes and Banados, Teitelboim and Zanelli Black Holes

2018 ◽  
Vol 73 (11) ◽  
pp. 1061-1073 ◽  
Author(s):  
N.A. Hussein ◽  
D.A. Eisa ◽  
T.A.S. Ibrahim
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Quantum Correction ◽  
Kerr Black Hole ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Charged Black Holes ◽  
Thermodynamic Variables

AbstractThis paper aims to obtain the thermodynamic variables (temperature, thermodynamic volume, angular velocity, electrostatic potential, and heat capacity) corresponding to the Schwarzschild black hole, Reissner-Nordstrom black hole, Kerr black hole and Kerr-Newman-Anti-de Sitter black hole. We also obtained the free energy for black holes by using three different methods. We obtained the equation of state for rotating Banados, Teitelboim and Zanelli black holes. Finally, we used the quantum correction of the partition function to obtain the heat capacity and entropy in the quantum sense.

scholarly journals THERMODYNAMIC GEOMETRY AND CRITICAL BEHAVIOR OF BLACK HOLES

2007 ◽  
Vol 22 (01) ◽  
pp. 11-27 ◽  
Author(s):  
JIANYONG SHEN ◽  
RONG-GEN CAI ◽  
BIN WANG ◽  
RU-KENG SU
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Critical Behavior ◽  
Hessian Matrix ◽  
Black Hole Entropy ◽  
De Sitter ◽  
Ads Black Holes ◽  
Gas System ◽  
The One

Based on the observations that there exists an analogy between the Reissner–Nordström–Anti-de Sitter (RN–AdS) black holes and the van der Waals–Maxwell liquid-gas system, in which a correspondence of variables is (ϕ,q) ↔ (V,P), we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN–AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN–AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.

scholarly journals Anti-de-Sitter-Maxwell-Yang-Mills Black Holes Thermodynamics from Nonlocal Observables Point of View

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
H. El Moumni
Keyword(s):  
Black Hole ◽  
Phase Structure ◽  
Entanglement Entropy ◽  
Point Of View ◽  
De Sitter ◽  
Yang Mills ◽  
Fixed Charges ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Grand Canonical

In this paper we analyze the thermodynamic properties of the Anti-de-Sitter black hole in the Einstein-Maxwell-Yang-Mills-AdS gravity (EMYM) via many approaches and in different thermodynamical ensembles (canonical/grand canonical). First, we give a concise overview of this phase structure in the entropy-thermal diagram for fixed charges and then we investigate this thermodynamical structure in fixed potentials ensemble. The next relevant step is recalling the nonlocal observables such as holographic entanglement entropy and two-point correlation function to show that both observables exhibit a Van der Waals-like behavior in our numerical accuracy and just near the critical line as the case of the thermal entropy for fixed charges by checking Maxwell’s equal area law and the critical exponent. In the light of the grand canonical ensemble, we also find a newly phase structure for such a black hole where the critical behavior disappears in the thermal picture as well as in the holographic one.

scholarly journals Stability of Schwarzschild (Anti)de Sitter black holes in conformal gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Daniele Lanteri ◽  
Shen-Song Wan ◽  
Alfredo Iorio ◽  
Paolo Castorina
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Geometrical Approach ◽  
Conformal Gravity ◽  
De Sitter ◽  
Weyl Gravity ◽  
Definite Answer ◽  
Thermodynamic Geometry ◽  
Thermodynamic Variables ◽  
Extensive Quantity

AbstractWe study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as thermodynamic geometry; (iv) the Poincaré method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first two methods, (i) and (ii), indicate that the entropy of a de Sitter black hole is always in the interval $$2/3\le S\le 1$$ 2 / 3 ≤ S ≤ 1 , whereas thermodynamic geometry suggests that, at $$S=1$$ S = 1 , there is a second order phase transition to an Anti de Sitter black hole. On the other hand, we obtain from the Poincaré method (iv) that black holes whose entropy is $$S < 4/3$$ S < 4 / 3 are stable or in a saddle-point, whereas when $$S>4/3$$ S > 4 / 3 they are always unstable, hence there is no definite answer on whether such transition occurs. Since thermodynamics geometry takes the view that the entropy is an extensive quantity, while the Poincaré method does not require extensiveness, it is valuable to present here the analysis based on both approaches, and so we do.

Thermodynamics of charged A(dS) black holes with quadratically-extended electrodynamics

2020 ◽  
Vol 17 (02) ◽  
pp. 2050020 ◽  
Author(s):  
M. Dehghani
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Electric Potential ◽  
Mass Formula ◽  
Black Hole Entropy ◽  
De Sitter ◽  
Two Phase ◽  
New Class ◽  
Hole Charge ◽  
Complete Set

In this paper, the Einstein-nonlinear electromagnetic theory has been studied in the four-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes. A new class of nonlinearly charged A(dS) black hole solution, in the presence of quadratically-extended Maxwell field, has been obtained and the thermodynamical properties have been analyzed. The black hole entropy, temperature and electric potential have been calculated, making use of the geometric methods. Through a Smarr mass formula the black hole mass has been written as a function of the complete set of extensive parameters (i.e. charge and entropy). It has been found that the intensive parameters (i.e. electric potential and temperature) obtained from the mass formula coincide with their values obtained from geometric approaches. It confirms the validity of the first law of black hole thermodynamics. A black hole stability analysis has been performed from the canonical ensemble approach, regarding the black hole heat capacity with the black hole charge as a constant. The points of type one and type two phase transitions, and the ranges at which the new charged A(dS) black holes are locally stable have been determined. Also, for the new charged black holes to be physically reasonable, their charge has been restricted to some specific ranges.

Thermodynamic stability of a regular black hole in nonlinear electrodynamics

2016 ◽  
Vol 94 (4) ◽  
pp. 425-430
Author(s):  
L.A. López ◽  
A. Eunice Matias
Keyword(s):  
Black Hole ◽  
Thermodynamic Stability ◽  
Turning Point ◽  
Canonical Ensemble ◽  
Point Method ◽  
Nonlinear Electrodynamics ◽  
Regular Black Hole ◽  
Maximum Value ◽  
Canonical Ensembles ◽  
Grand Canonical

By the turning point method, we study the thermodynamic stability of the a regular black hole in nonlinear electrodynamics. The microcanonical, canonical, and grand canonical ensembles are analyzed; the phase diagrams (m, βm) and (q, βq) (microcanonical ensemble) show that the regular black hole is stable at all the equilibrium sequence, but for the phase diagram (βm, –m) (canonical and grand canonical ensembles) the black hole shows a turning point. This means that the black hole is thermodynamically unstable. The temperature of the regular black hole has behavior that resembling Reissner–Nordstrom behavior: the temperature grows with the mass as in an ordinary thermodynamical system, but there is a maximum value of mass beyond which the temperature diminishes. The heat capacity displays a divergence with a change of sign that occurs precisely at the turning point obtained by the turning point method in the canonical ensemble.

Statistical mechanics

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Statistical Mechanics ◽  
Potential Model ◽  
Quantum Corrections ◽  
Inhomogeneous Systems ◽  
Hard Constraints ◽  
Complex Liquids ◽  
Fluid Membranes ◽  
Dynamical Properties ◽  
Canonical Ensembles ◽  
Grand Canonical

This chapter contains the essential statistical mechanics required to understand the inner workings of, and interpretation of results from, computer simulations. The microcanonical, canonical, isothermal–isobaric, semigrand and grand canonical ensembles are defined. Thermodynamic, structural, and dynamical properties of simple and complex liquids are related to appropriate functions of molecular positions and velocities. A number of important thermodynamic properties are defined in terms of fluctuations in these ensembles. The effect of the inclusion of hard constraints in the underlying potential model on the calculated properties is considered, and the addition of long-range and quantum corrections to classical simulations is presented. The extension of statistical mechanics to describe inhomogeneous systems such as the planar gas–liquid interface, fluid membranes, and liquid crystals, and its application in the simulation of these systems, are discussed.

Sign in / Sign up

Export Citation Format

Share Document