Thermodynamics of a Sufficient Small Singly Spinning Kerr-AdS Black Hole

TL;DR

This paper investigates how thermal fluctuations affect the thermodynamics and stability of small singly spinning Kerr-AdS black holes, revealing significant corrections to entropy and implications for critical phenomena.

Contribution

It introduces a logarithmic correction to the entropy of small Kerr-AdS black holes due to thermal fluctuations, impacting their thermodynamic stability and critical behavior.

Findings

Logarithmic entropy correction becomes significant for small black holes.

Thermal fluctuations influence the stability and phase structure.

Critical phenomena are affected by the entropy corrections.

Abstract

In this paper, we will analyze the thermodynamics of a small singly spinning Kerr-AdS black hole. As the black hole will be sufficient small, its temperature will be large and so we can not neglect the effects of thermal fluctuations. We will demonstrate that these thermal fluctuations correct the entropy of singly spinning Kerr-AdS black hole by a logarithmic correction term. We will analyze the implications of the logarithmic correction on other thermodynamic properties of this black hole, and analyze the stability of such a black hole. We will observe that this form of correction becomes important when the size of the black hole is sufficient small. We will also analyze the effect of these thermal fluctuations on the critical phenomena for such a black hole.