Exact Spherically Symmetric Solutions in Massive Gravity

TL;DR

The paper addresses how to construct a viable infrared modification of gravity by coupling our metric to an extra spin-2 field, yielding a Lorentz-breaking bigravity theory. It develops exact non-linear, static, spherically symmetric solutions that generalize Schwarzschild and reveal a novel power-law correction $S\,r^{\gamma}$ and a source-size dependent mass shift, signaling a dynamical violation of the Strong Equivalence Principle. The analysis shows that linearized results fail to capture the full IR behavior, and it explores decoupling and Lorentz-invariant limits, finding a well-behaved LI phase with massless gravitons but distinct non-perturbative structure. The findings have implications for the phenomenology of massive gravity, including potential astrophysical effects, local Lorentz violation near sources, and cosmological considerations, while leaving stability and Vainshtein-type issues as avenues for further study.

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.