Exponential corrected thermodynamics of black holes

TL;DR

This paper investigates how exponential quantum corrections due to thermal fluctuations affect black hole thermodynamics, revealing stability conditions and modifications to mass, entropy, and phase behavior across various black hole types.

Contribution

It introduces exponential quantum corrections into black hole thermodynamics and analyzes their impact on stability, mass, and thermodynamic relations for different black hole solutions.

Findings

Thermal fluctuations decrease Schwarzschild black hole mass.

Quantum corrections can stabilize small Schwarzschild black holes.

5D Schwarzschild black holes remain unstable under quantum corrections.

Abstract

Recently, it is reported that thermal fluctuations, which are interpreted as quantum effects, modify the black holes entropy by an exponential term. We now find the effect of such modification on the black hole mass and other thermodynamics quantities. We find that the Schwarzschild black hole mass decreased by thermal fluctuations. Hence, we study exponential corrected thermodynamics and statistics of black holes by computing the partition function. We obtain the special condition on the event horizon radius to satisfy Smarr-Gibbs-Duhem relation in the presence of quantum correction. As we know, the Schwarzschild black hole is unstable, while the effect of exponential correction is the stability of $4D$ Schwarzschild black hole as well as the Schwarzschild-AdS black hole at a small area. On the other hand, a $5D$ Schwarzschild black hole is completely unstable. The effect of the quantum correction on the Reissner-Nordstr\"{o}m black hole is instability at quantum scales. Finally, we consider the most general case of charged AdS black hole and study the corrected thermodynamics.