Thermodynamic Studies with Higher-Order Quantum Corrected Entropy: Higher Dimensional Gauss-Bonnet Black Holes

In addition to the classical definition of the black hole's entropy, quantum mechanics requires several modifications of it. In this article, we consider the higher-order quantum correction in entropy and analyze the thermodynamic properties of a black hole solution which is sitting in one of the modified gravity theories, viz. Gauss-Bonnet gravity, in this point of view. Here mainly two thermodynamic potentials, Gibbs free energy and Helmholtz free energy are studied. As both potentials are very much important to investigate small/large black hole phase transition. Presenting the variations of higher-order corrected Gibbs free energy and Helmholtz free energy in different conditions, we analyze the phase transition and critical behavior of said black holes. We also re-examine our results, with the P-V criticality analyses and study P - r(+ )diagrams. Moreover, we compute the critical temperature, pressure and volume and the relation among them. Here we find an interesting result for Q = 0 and for the Ricci flat horizon of this black hole that the relation is exactly equal to the result obtained for the van der Waals system. Further, we study thermal stability by computing the specific heat with higher-order correction and explain it by depicting the C(HC )vs r(+ )diagrams in different conditions.

Automated summary

In this article, the thermodynamic properties of a black hole solution in Gauss-Bonnet gravity are analyzed by studying the variations of Gibbs free energy and Helmholtz free energy. The phase transition and critical behavior of the black holes are examined and a relation similar to the van der Waals system is found. The thermal stability is also investigated by computing the specific heat with higher-order correction.