Spherically symmetric black holes in metric gravity

TL;DR

This paper investigates the conditions under which modified theories of gravity can support spherically symmetric black holes, analyzing their properties and providing methods to construct solutions beyond GR.

Contribution

It derives constraints for modified gravity theories to admit black hole solutions similar to those in GR and explores both perturbative and nonperturbative solutions.

Findings

Identifies conditions for black hole existence in modified gravity

Analyzes properties of solutions in the Starobinsky model

Provides methods for constructing nonperturbative solutions

Abstract

The existence of black holes is one of the key predictions of general relativity (GR) and therefore a basic consistency test for modified theories of gravity. In the case of spherical symmetry in GR the existence of an apparent horizon and its regularity is consistent with only two distinct classes of physical black holes. Here we derive constraints that any self-consistent modified theory of gravity must satisfy to be compatible with their existence. We analyze their properties and illustrate characteristic features using the Starobinsky model. Both of the GR solutions can be regarded as zeroth-order terms in perturbative solutions of this model. We also show how to construct nonperturbative solutions without a well-defined GR limit.