Thermal properties of black hole Reissner-Nordstr¨om

Abstract

Based on the metric of the Reissner-Nordstr¨om charged black hole was found analytic expressions for the temperature, pressure and volume of the black hole. The numerical results
prove that at temperatures less than the critical temperature Tc, the matter outside black hole is similar to Van der Walls real gas in that it can exist in gas or liquid phase and a gas-liquid phase
transition may occur when the volume (or radius of the horizon) of black hole changes. Opposite, when the temperature is greater than Tc, the mater can only be in the gas phase. This result is consistent with the known result.