Hawking decay and thermodynamic transformation of a black hole: two examples

Abstract

The criterion for thermodynamic stability of rotating electrically charged quantum black holes was already derived by us. They appeared as a collection of inequalities connecting second-order derivatives of the black hole mass with respect to its horizon area, electric charge and angular momentum. We got similar results when this analysis was extended to black holes in arbitrary dimensional spacetime with any number of parameters that determine the mass of the black hole. Many black holes were shown to satisfy some of the stability criteria in certain regions of parameter space, but not all together. They are known as “Quasi Stable” black holes. Quasi stability restricts the accessibility of parameter space; hence, it creates bounds on various parameters of the quasi-stable black holes. They, although decaying under Hawking radiation, possess bounded fluctuations in certain regions of their accessibility for some of their parameters. We here consider Kerr–Newman and Kerr–Sen black holes as examples of two quasi-stable black holes. Their fluctuations are shown to be related to the bounds in parameter space. We also study the decay rate in various regions of their parameter spaces. We conclude that they transform to different kinds of black holes during their Hawking decay.