Thermodynamical instability of black holes

In contrast to Hawking radiation of black hole with a given spacetime structure, we consider a competitive transition due to a heat transfer from a hotter inner horizon to a colder outer horizon of Kerr black hole, that results in a stable thermodynamical state of extremal black hole. In this process, by supposing an emission of gravitational quanta, we calculate the mass of extremal black hole in the final state of transition.