Black holes in modified gravity theories

TL;DR

This paper investigates black hole solutions within $f(R)$ gravity theories, finding that only Schwarzschild-(Anti-) de Sitter type solutions emerge perturbatively, and explores their thermodynamic stability in Anti-de Sitter space.

Contribution

It provides explicit perturbative solutions for black holes in $f(R)$ gravity and analyzes their thermodynamic properties and stability.

Findings

Solutions are of Schwarzschild-(Anti-) de Sitter type up to second order in perturbation.

Explicit expressions for solutions are derived in terms of the $f(R)$ function.

Black holes in Anti-de Sitter space exhibit specific thermodynamic stability characteristics.

Abstract

In the context of $f(R)$ gravity theories, the issue of finding static and spherically symmetric black hole solutions is addressed. Two approaches to study the existence of such solutions are considered: first, constant curvature solutions, and second, the general case (without imposing constant curvature) is also studied. Performing a perturbative expansion around the Einstein-Hilbert action, it is found that only solutions of the Schwarzschild-(Anti-) de Sitter type are present (up to second order in perturbations) and the explicit expressions for these solutions are provided in terms of the $f(R)$ function. Finally we consider the thermodynamics of black holes in Anti-de Sitter space-time and study their local and global stability.