Restricted Phased Space Thermodynamics for Black Holes in Higher Dimensions and Higher Curvature Gravities

Abstract

The recently proposed restricted phase space thermodynamics is shown to be applicable to a large class of higher dimensional higher curvature gravity models coupled to Maxwell field, which are known as black hole scan models and are labeled by the spacetime dimension d and the highest order k of the Lanczos-Lovelock densities appearing in the action. Three typical example cases with (d,k)=(5,1),(5,2) and (6,2) are chosen as example cases and studied in some detail. These cases are representatives of Einstein-Hilbert, Chern-Simons and Born-Infield like gravity models. Our study indicates that the Einstein-Hilbert and Born-Infield like gravity models have similar thermodynamic behaviors, e.g., the existence of isocharge T−S phase transitions with the same critical exponents, the existence of isovoltage T−S transitions and the Hawking-Page like transitions, and the similar high temperature asymptotic behaviors for the isocharge heat capacities, etc. However, the Chern-Simons like (5,2)-model behaves quite differently. Neither isocharge nor isovoltage T−S transitions could occur and no Hawking-Page like transition is allowed. This seems to indicate that the Einstein-Hilbert and Born-Infield like models belong to the same universality class while the Chern-Simons like models do not.

Rate of the phase transition for a charged anti-de Sitter black hole

“…Through the analogy analysis with van der Waals fluid, people believe that the (theoretical) black hole has a certain microstructure [14][15][16][17][18][19][20]. Meanwhile, some recent studies [21][22][23][24][25][26][27][28][29] are devoted to using the anti-de Sitter/conformal field theory correspondence to explore the physical explanation of black hole thermodynamics in the field theory and make the relevant concepts of black hole thermodynamics reasonably and reliably.…”

4D-EGB Black Holes in RPS Thermodynamics

“…The central charge is related to the Newton's constant G and the AdS curvature radius l via C = l d−2 /G, where d is the dimension of the AdS space-time [21,22]. Homogeneity of Smarr relation, thermodynamic processes and phase transitions, were studied in the RN-AdS, Kerr-AdS, BTZ and Taub-NUT black holes in the context of RPST [21,[23][24][25][26].…”

“…This motivates us to consider the RPST formalism in the 4D-EGB gravity background. A second motivation is to study effects of the Gauss-Bonnet constant on thermodynamic behaviors of a charged and uncharged black holes in both approaches and to complete the study of black holes in the RPST formalism already made in [21,[23][24][25][26].…”

Rate of the phase transition for a charged anti-de Sitter black hole

“…Through the analogy analysis with van der Waals fluid, people believe that the (theoretical) black hole has a certain microstructure [14][15][16][17][18][19][20]. Meanwhile, some recent works [21][22][23][24][25][26][27][28][29] are devoted to using the anti-de Sitter/conformal field theory correspondence to explore the physical explanation of black hole thermodynamics in the field theory and make the relevant concepts of black hole thermodynamics reasonably and reliably.…”