scholarly journals On the equipartition theorem and black holes non-Gaussian entropies

2020 ◽  
Vol 35 (32) ◽  
pp. 2050266 ◽  
Author(s):  
Everton M. C. Abreu ◽  
Jorge Ananias Neto ◽  
Edésio M. Barboza ◽  
Albert C. R. Mendes ◽  
Bráulio B. Soares
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
Algebraic Expression ◽  
Mathematical Form ◽  
Entropy Model ◽  
Standard Thermodynamic Functions ◽  
Mathematical Expressions ◽  
Equipartition Theorem ◽  
Non Gaussian

In this letter we have shown that, from the standard thermodynamic functions, the mathematical form of an equipartition theorem may be related to the algebraic expression of a particular entropy initially chosen to describe the black hole event horizon. Namely, we have different equipartition expressions for distinct statistics. To this end, four different mathematical expressions for the entropy have been selected to demonstrate our objective. Furthermore, a possible phase transition is observed in the heat capacity behavior of the Tsallis and Cirto entropy model.

scholarly journals P–V criticality and geometrical thermodynamics of black holes with Born–Infeld type nonlinear electrodynamics

2016 ◽  
Vol 25 (01) ◽  
pp. 1650010 ◽  
Author(s):  
S. H. Hendi ◽  
S. Panahiyan ◽  
B. Eslam Panah
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
Phase Space ◽  
Critical Behavior ◽  
Nonlinear Electrodynamics ◽  
Extended Phase Space ◽  
Maxwell Theory ◽  
Extended Phase ◽  
Transition Points

In this paper, we take into account the black-hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant as a dynamical pressure to study the phase transitions and analogy of the black holes with the Van der Waals liquid–gas system in the extended phase space. We make a comparison between linear and nonlinear electrodynamics and show that the lowest critical temperature belongs to Maxwell theory. Also, we make some arguments regarding how power of nonlinearity brings the system to Schwarzschild-like and Reissner–Nordström-like limitations. Next, we study the critical behavior of the system in the context of heat capacity. We show that critical behavior of system is similar to the one in phase diagrams of extended phase space. We also extend the study of phase transition points through geometrical thermodynamics (GTs). We introduce two new thermodynamical metrics for extended phase space and show that divergencies of thermodynamical Ricci scalar (TRS) of the new metrics coincide with phase transition points of the system. Then, we introduce a new method for obtaining critical pressure and horizon radius by considering denominator of the heat capacity.

scholarly journals Thermodynamic properties of black holes in de Sitter space

2016 ◽  
Vol 32 (02) ◽  
pp. 1750017 ◽  
Author(s):  
Huai-Fan Li ◽  
Meng-Sen Ma ◽  
Ya-Qin Ma
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Quantities ◽  
De Sitter ◽  
First Law Of Thermodynamics ◽  
Effective Temperatures ◽  
Sds Black Hole

We study the thermodynamic properties of Schwarzschild–de Sitter (SdS) black hole and Reissner–Nordström–de Sitter (RNdS) black hole in view of global and effective thermodynamic quantities. Making use of the effective first law of thermodynamics, we can derive the effective thermodynamic quantities of de Sitter black holes. It is found that these effective thermodynamic quantities also satisfy Smarr-like formula. Especially, the effective temperatures are nonzero in the Nariai limit. By calculating heat capacity and Gibbs free energy, we find SdS black hole is always thermodynamically stable and RNdS black hole may undergoes phase transition at some points.

scholarly journals On a Model of Magnetically Charged Black Hole with Nonlinear Electrodynamics

Universe ◽  
2018 ◽  
Vol 4 (5) ◽  
pp. 66 ◽  
Author(s):  
Sergey Kruglov
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
General Relativity ◽  
Black Hole ◽  
Order Phase Transition ◽  
Nonlinear Electrodynamics ◽  
Magnetic Mass ◽  
Metric Function ◽  
Second Order Phase Transition

The Bronnikov model of nonlinear electrodynamics is investigated in general relativity. The magnetic black hole is considered and we obtain a solution giving corrections to the Reissner-Nordström solution. In this model spacetime at r → ∞ becomes Minkowski’s spacetime. We calculate the magnetic mass of the black hole and the metric function. At some parameters of the model there can be one, two or no horizons. The Hawking temperature and the heat capacity of black holes are calculated. We show that a second-order phase transition takes place and black holes are thermodynamically stable at some range of parameters.

scholarly journals Magnetically charged black hole in framework of nonlinear electrodynamics model

2018 ◽  
Vol 33 (03) ◽  
pp. 1850023 ◽  
Author(s):  
S. I. Kruglov
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
General Relativity ◽  
Black Hole ◽  
Regular Solution ◽  
Nonlinear Electrodynamics ◽  
Magnetic Mass ◽  
Thermodynamics Of Black Holes ◽  
Metric Function

A model of nonlinear electrodynamics is proposed and investigated in general relativity. We consider the magnetic black hole and find a regular solution which gives corrections into the Reissner–Nordström solution. At [Formula: see text] the asymptotic space–time becomes flat. The magnetic mass of the black hole is calculated and the metric function is obtained. At some values of the model parameter there can be one, two or no horizons. Thermodynamics of black holes is studied and we calculate the Hawking temperature and heat capacity of black holes. It is demonstrated that there is a phase transition of second order. At some parameters of the model black holes are thermodynamically stable.

scholarly journals Geometrical Method for Thermal Instability of Nonlinearly Charged BTZ Black Holes

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Seyed Hossein Hendi ◽  
Shahram Panahiyan ◽  
Behzad Eslam Panah
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
Three Dimensional ◽  
Nonlinear Electrodynamics ◽  
Geometrical Approach ◽  
Divergence Point ◽  
Btz Black Holes ◽  
Transition Points ◽  
The Stability

We consider three-dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic, and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity, whereas, for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.

The thermodynamics of the divalent metal fluorides. I. Heat capacity of lead tetrafluorostannate, PbSnF4, from 10.3 to 352 K

1988 ◽  
Vol 66 (4) ◽  
pp. 549-552 ◽  
Author(s):  
Jane E. Callanan ◽  
Ron D. Weir ◽  
Edgar F. Westrum Jr.
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Thermodynamic Functions ◽  
Adiabatic Calorimetry ◽  
Temperature Limit ◽  
Divalent Metal ◽  
Ion Conductor ◽  
Metal Fluorides ◽  
Fast Ion Conductor ◽  
Fast Ion

We have measured the heat capacity of the fast ion conductor PbSnF4 at 10.3 < T < 352 K by adiabatic calorimetry. Our results show anomalous values in the Cp,m in the region 300 < T < 352 K. These are associated with the α–β crystallographic transition reported at 353 K. Because the upper temperature limit of our cryostat is around 354 K, it was impossible to follow the phase transition to completion. A more subtle anomaly in the Cp,m was detected between 130 and 160 K. Standard molar thermodynamic functions are presented at selected temperatures from 5 to 350 K.

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