Quantum gravity effects on the thermodynamic stability of 4D Schwarzschild black hole

Abstract

Based on the Euclidean approach, we consider the effects of quantum gravity and mass-less matter on the thermodynamic properties of Schwarzschild black hole. The techniques of effective field theory are utilized to analytically construct the partition function at the one-loop level. Using the non-local heat kernel formalism, the partition function is expressed as a curvature expansion. We extensively discuss the effect of the corrections on the thermodynamic stability. The one-loop free energy shows, remarkably, that a large number of gauge fields is able to render Schwarzschild black hole thermodynamically stable. The black hole mass at which stability is achieved scales as $\sqrt{N}$ in Planck units, where $N$ is the number of gauge fields, and is independent of any UV completion of quantum gravity.