Equations-of-state deduced form different types of black holes

Black holes are seen as thermodynamical systems. They can be characterized by thermodynamic intensive quantities such as temperature, pressure, and extensive quantities such as entropy and energy density. In this paper, we focus on the thermodynamical properties of (a) Schwarzschild, (b) Reissner–Nordström, (c) Kerr, and (d) Kerr–Newman black holes. These allow to estimate the corresponding equations-of-state (EoS) and the squared speed of sound for each of them. The latter helps to calculate the ratio of the bulk viscosity to the shear viscosity for each of the black holes. We conclude that the resulting EoS enhances when moving from Schwarzschild to Reissner–Nordström to Kerr, and to Kerr–Newman black holes.