Physical black holes in fourth-order gravity

TL;DR

This paper explores how fourth-order gravity theories, including f(R) models, can produce black hole solutions similar to those in general relativity, challenging the uniqueness of observational signatures of black holes.

Contribution

It demonstrates that fourth-order gravity theories naturally admit black hole solutions, complicating the distinction between general relativity and modified gravity based solely on horizon observations.

Findings

Fourth-order gravity theories accommodate both classes of black hole solutions.

Observation of apparent horizons may not distinguish between GR and modified gravity.

Modified gravity terms can mimic black hole formation scenarios of general relativity.

Abstract

The existence of black holes is a central prediction of general relativity and thus serves as a basic consistency test for modified theories of gravity. In spherical symmetry, only two classes of dynamic solutions are compatible with the formation of an apparent horizon in finite time of a distant observer. Moreover, the formation of black holes follows a unique scenario involving both types of solutions. To be compatible with their existence, any self-consistent theory of modified gravity must satisfy several constraints. We derive properties of the modified gravity terms of f(R) and generic fourth-order gravity theories and find that they naturally accommodate both classes of solutions. Consequently, the observation of an apparent horizon by itself may not suffice to distinguish between general relativity and modifications including up to fourth-order derivatives in the metric.