Black hole entropy in string-generated gravity models

TL;DR

This paper calculates the entropy of black holes in string-inspired gravity models with quadratic curvature terms, showing that entropy remains positive for certain horizon curvatures and linking it to energy conditions.

Contribution

It introduces a method to compute black hole entropy in string-generated quadratic gravity models and analyzes the positivity conditions for different horizon curvatures.

Findings

Black hole entropy is positive for flat and spherical horizons.

Extremal hyperbolic black holes have non-negative entropy under energy conditions.

Negative mass extremal metrics serve as backgrounds for hyperbolic black holes.

Abstract

The Euclidean action and entropy are computed in string-generated gravity models with quadratic curvatures, and used to argue that a negative mass extremal metric is the background for hyperbolic (k=-1) black hole spacetimes, k being the curvature constant of the event horizon. The entropy associated with a black hole is always positive for k=(0,1) family. The positivity of energy condition also ensures that the k=-1 (extremal) entropy is non-negative.