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

## TL;DR

This paper investigates how quantum gravity and matter influence the thermodynamic stability of Schwarzschild black holes, revealing that numerous gauge fields can stabilize the black hole thermodynamically.

## Contribution

It analytically demonstrates that quantum corrections from gauge fields can stabilize Schwarzschild black holes, with stability depending on the number of gauge fields and independent of UV quantum gravity details.

## Key findings

- Large number of gauge fields stabilizes black hole thermodynamics.
- Black hole mass for stability scales as √N in Planck units.
- Quantum corrections are computed using effective field theory and heat kernel methods.

## 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.