#Heat capacity of grand canonical ensemble

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Consequences of Thermal Fluctuations of Well-Known Black Holes in Modified Gravity. (arXiv:2008.11033v1 [gr-qc])

Quantum fluctuation consequences have significant role in high-energy physics. These fluctuation often regarded as a correction of the infrared (IR) limit. Such correction contribute to the high-energy limit of thermodynamical quantities and the stability conditions of black holes. In this work, we analyze the thermal stability of black holes in the presence of thermal fluctuations. We consider AdS black hole in Born-Infeld massive gravity with non-abelian hair and the charged AdS black hole with a global monopole. We develop many thermodynamical quantities such as entropy, temperature, pressure, heat capacity of a system at constant volume and pressure, ratio between the heat capacities at constant pressure and volume, Gibbs free energy and Helmholtz free energy for both black holes. The critical behavior and phase transitions of black holes are also presented. We also observe the local and global stability of black holes in the grand canonical ensemble and canonical ensemble for the specific values of different parameters, such as, symmetry breaking parameter $\eta$, massive parameter $m$ and non-abelian hair $\nu$.

from gr-qc updates on arXiv.org https://ift.tt/32noCcc

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Dilaton black holes with power law electrodynamics. (arXiv:1906.11063v1 [gr-qc])

In this article, the new black hole solutions to the Einstein-power-Maxwell-dilaton gravity theory have been investigated in a four-dimensional space-time. The coupled scalar, electromagnetic and gravitational field equations have been solved in a static and spherically symmetric geometry. It has been shown that dilatonic potential, as the solution to the scalar field equation, can be written in the form of a generalized Liouville potential. Also, three classes of novel charged dilaton black hole solutions, in the presence of power law nonlinear electrodynamics, have been constructed out which are asymptotically non-flat and non-AdS. The conserved and thermodynamic quantities have been calculated from geometrical and thermodynamical approaches, separately. Since the results of these two alternative approaches are identical one can argue that the first law of black hole thermodynamics is valid for all of the new black hole solutions. The thermodynamic stability or phase transition of the black holes have been studied, making use of the canonical ensemble method. The points of type-1 and type-2 phase transitions as well as the ranges at which the black holes are stable have been indicated by considering the heat capacity of the new black hole solutions. The global stability of the black holes have been studied through the grand canonical ensemble method. Regarding the Gibbs free energy of the black holes, the points of Hawking-Page phase transition and ranges of the horizon radii at which the black holes are globally stable have been determined.

from gr-qc updates on arXiv.org https://ift.tt/2KICtDA

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Thermodynamics of Black holes With Higher Order Corrected Entropy. (arXiv:1811.10873v1 [gr-qc])

For analyzing the thermodynamical behavior of two well-known black holes such as 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 heats, pressure, Gibb's and Helmhotz free energies for both black holes in the presence of corrected entropy. The versatile study on the stability of black holes is being made by using various frameworks such as the ratio of heat capacities ($\gamma$), 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.

from gr-qc updates on arXiv.org https://ift.tt/2zxeIae

[arxt1]

Effects of Thermal Fluctuations on Non-minimal Regular Magnetic Black Hole. (arXiv:1705.10012v1 [gr-qc])

We analyze the effects of thermal fluctuations on a regular black hole (RBH) of non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations corresponding to non-minimal RBH thermodynamics. In this scenario, we develop various important thermodynamical quantities such as entropy, pressure, specific heats, Gibb's free energy and Helmothz free energy. We investigate first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal RBH. We also discuss the stability of this RBH using various frameworks such as $\gamma$ factor (comprises of ratio of heat capacities), phase transition, grand canonical ensemble and canonical ensemble. It is observed that the non-minimal RBH becomes more globally and locally stable if we increase the value of cosmological constant.

from gr-qc updates on arXiv.org http://ift.tt/2rehcVG