Constraining modified gravity theories with physical black holes

TL;DR

This paper reviews the constraints on modified gravity theories to ensure compatibility with black hole solutions in semiclassical gravity, highlighting that many such theories cannot be distinguished observationally based solely on apparent horizon observations.

Contribution

It demonstrates that generic fourth-order modified gravity theories satisfy semiclassical black hole constraints, making observational differentiation challenging.

Findings

Modified gravity theories with up to fourth-order derivatives satisfy black hole constraints.

Semiclassical solutions are zeroth-order in perturbative expansions of these models.

Observations of apparent horizons alone may not distinguish between theories.

Abstract

We review the constraints modified theories of gravity must satisfy to be compatible with the spherically symmetric black hole solutions of semiclassical gravity that describe the formation of an apparent horizon in finite time of a distant observer. The constraints are satisfied in generic modified gravity theories with up to fourth-order derivatives in the metric, indicating that the semiclassical solutions correspond to zeroth-order terms in perturbative solutions of these models. From an observational point of view, this result implies that it may not be possible to distinguish between the semiclassical theory and modifications including up to fourth-order derivatives based on the observation of an apparent horizon alone.