Exact Solutions in Massive Gravity

TL;DR

This paper reviews exact solutions in massive gravity, focusing on static black holes and self-accelerating cosmological backgrounds, highlighting their stability and ability to mimic General Relativity near sources.

Contribution

It provides a comprehensive classification of static and self-accelerating solutions in massive gravity, including black holes and cosmological models, with stability analysis.

Findings

Black hole configurations that recover GR near sources

Self-accelerating cosmological solutions with stability analysis

Massive gravity solutions can mimic GR and explain cosmic acceleration

Abstract

Massive gravity is a good theoretical laboratory to study modifications of General Relativity. The theory offers a concrete set-up to study models of dark energy, since it admits cosmological self-accelerating solutions in the vacuum, in which the size of the acceleration depends on the graviton mass. Moreover, non-linear gravitational self-interactions, in the proximity of a matter source, manage to mimic the predictions of linearised General Relativity, hence agreeing with solar-system precision measurements. In this article, we review our work in the subject, classifying, on one hand, static solutions, and on the other hand, self-accelerating backgrounds. For what respects static solutions we exhibit black hole configurations, together with other solutions that recover General Relativity near a source via the Vainshtein mechanism. For the self-accelerating solutions we describe a wide class of cosmological backgrounds, including an analysis of their stability.