Thermodynamics of asymptotically flat Reissner–Nordstrom black hole

Abstract

We established the criteria for thermal stability of a most general black hole in the form of a series of inequalities connecting second-order derivatives of the black hole mass with respect to its parameters. The mass of a black hole depends solely on these parameters, e.g. horizon area and electric charge are these parameters for non-rotating charged black hole. We also introduced the notion of “Quasi stability”. It is known how to calculate the fluctuations of these parameters for both stable and quasi stable black holes. In this paper, we consider the simplest black hole having nontrivial parameter, i.e. electrically charged non-rotating asymptotically flat Reissner–Nordstrom black hole (AFRNBH). We will show here that this black hole is not stable anywhere in its parameter space, but it is actually quasi stable, having positive specific heat in some region, violating Hawking’s prediction. In fact, this black hole will be shown to exhibit phase transition which is structurally quite different from that in case of Schwarzschild black hole, as predicted first by Hawking. This black hole will also be shown to try to resist its decay under Hawking radiation, but ultimately remains unsuccessful.