A new rotating black hole in quintessential dark energy and its thermodynamics

Abstract

The spacetime metric for a rotating black hole in a quintessential field can take various forms owing to the ambiguity of the state equation for quintessential dark energy in rotating spacetime. Herein, to provide a more physical solution, the metric is determined by imposing the laws of thermodynamics of a black hole, which is typically valid in most systems. The new metric ensures the validity of the first and second laws of thermodynamics and can degenerate to the known non-rotating metric in the quintessential field. Moreover, we set an upper limit for the black hole rotation parameter, $a$, in our metric according to the weak energy condition (WEC).