Analytic solutions in non-linear massive gravity

TL;DR

This paper explores spherically symmetric solutions in a covariant massive gravity model, revealing branches that recover General Relativity via the Vainshtein mechanism and others describing Schwarzschild-de Sitter spacetimes with curvature linked to graviton mass.

Contribution

It provides new analytic solutions in non-linear massive gravity, demonstrating the Vainshtein mechanism and exact Schwarzschild-de Sitter solutions within a ghost-free framework.

Findings

Vainshtein mechanism operates below the radius $(r_g m^2)^{1/3}$

Existence of Schwarzschild-de Sitter solutions with curvature proportional to graviton mass squared

Identification of solution branches in covariant massive gravity model

Abstract

We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering General Relativity below a Vainshtein radius given by $(r_g m^2)^{1/3}$, where $m$ is the graviton mass and $r_g$ is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to Schwarzschild-de Sitter spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.