Exact solutions in massive gravity

Abstract

Massive gravity is a good theoretical framework to study the 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, nonlinear gravitational self-interactions, in the proximity of a matter source, manage to mimic the predictions of linearized General Relativity; hence, agreeing with solar-system precision measurements. In this paper, we review our work in the subject, classifying, on one hand, static solutions, and on the other hand, self-accelerating backgrounds. For the 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.