Due to thermal radiation process, the temperature of the Schwarzschild black hole diverges at the time the black hole evaporates, while it is natural to expect a vanishing temperature, since the spacetime geometry becomes Minkowskian whose intrinsic temperature is identically zero. Recently, a nonsingular temperature has been proposed in this research line, which follows the Hawking temperature for the large black hole system, at the same time becomes null in the limiting case the black hole mass tends to zero. In this paper, the stability and the phase transition of the quantum-corrected Schwarzschild black hole are investigated based on this modified temperature. For that, the thermodynamic quantities like the local temperature, the heat capacity, and the off-shell free energy are calculated. The results show that the free energy of the black hole follows the characteristic swallow-tail behavior, implying the existence of an unstable intermediate black hole state quickly decaying into the stable small or large black hole.
Geodesic stability and quasi normal modes via Lyapunov exponent for Hayward black hole
