Logarithmic corrections to entropy for black holes with hyperbolic horizon

TL;DR

This paper calculates logarithmic entropy corrections for various hyperbolic horizon black holes across four and five dimensions, addressing issues with negative energies by introducing extremal background states.

Contribution

It introduces a method to compute logarithmic entropy corrections for hyperbolic horizon black holes using extremal backgrounds, extending previous approaches.

Findings

Logarithmic corrections are obtained for hyperbolic black holes in 4D and 5D.

Extremal black hole backgrounds resolve negative energy issues.

Corrections provide insights into black hole thermodynamics with hyperbolic horizons.

Abstract

We compute logarithmic corrections to entropy for black holes with hyperbolic horizon. For this purpose, we introduce the topological black hole and MTZ black holes in four dimensions, while in five dimensions, the topological black holes and Gauss-Bonnet black hole with negative coupling are considered. As they stand, logarithmic corrections are problematic because small black holes with positive heat capacity have negative energies. However, introducing the background state of extremal black hole, the logarithmic corrections are performed for black hole with hyperbolic horizon.