Thermodynamic and geometric framework of a (2+1)-dimensional black hole with non-linear electrodynamics

Abstract

Gang( ) a)b) † , Liu Zhan-Fang( ) a) , and Lan Ming-Jian( ) b)

Legendre transformations and the thermodynamic geometry of 5D black holes

“…For a thermodynamic system, it is quite interesting to investigate the corresponding relationship between the curvature of the Weinhold metric, the Ruppeiner metric and the Legendre invariant metric, and the phase transitions. In fact the above viewpoints have been applied to various black holes [27][28][29][30][31][32], even though it is widely believed that the thermodynamic geometry of a black hole is still a most fascinating and unresolved subject at present. The main purpose of the present work is to show that the Legendre invariant metric can be used to correctly reproduce the thermodynamics of the 5D black hole and the EMGB black hole.…”