Exact Spherically Symmetric Solutions in Massive Gravity

TL;DR

This paper derives exact spherically symmetric solutions in a version of massive gravity coupled to an extra spin-two field, revealing modifications to the Schwarzschild metric including mass shifts and new power-law terms.

Contribution

It provides the first exact solutions for static spherically symmetric bodies in a ghost-free massive gravity theory with an additional spin-two field.

Findings

Presence of a mass shift in the gravitational field.

Existence of a new power-like term influenced by the source.

Violation of the Strong Equivalence Principle depending on source and coupling.

Abstract

A phase of massive gravity free from pathologies can be obtained by coupling the metric to an additional spin-two field. We study the gravitational field produced by a static spherically symmetric body, by finding the exact solution that generalizes the Schwarzschild metric to the case of massive gravity. Besides the usual 1/r term, the main effects of the new spin-two field are a shift of the total mass of the body and the presence of a new power-like term, with sizes determined by the mass and the shape (the radius) of the source. These modifications, being source dependent, give rise to a dynamical violation of the Strong Equivalence Principle. Depending on the details of the coupling of the new field, the power-like term may dominate at large distances or even in the ultraviolet. The effect persists also when the dynamics of the extra field is decoupled.