Spherically Symmetric Solutions in Ghost-Free Massive Gravity

TL;DR

This paper explores spherically symmetric solutions in ghost-free massive gravity, revealing two solution branches with distinct properties, including Schwarzschild-like and Yukawa-modified potentials, emphasizing the importance of bigravity formulation.

Contribution

It provides a detailed analysis of spherically symmetric solutions in ghost-free massive gravity, highlighting the existence of two branches and the significance of bigravity.

Findings

First branch solutions are Schwarzschild-like with no modifications.

Second branch solutions exhibit Yukawa-like potential modifications.

Bigravity formulation is essential for understanding these solutions.

Abstract

Recently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz invariant and a Lorentz breaking asymptotically flat behaviour and also fall in two branches. In the first branch, all solutions can be found analitycally and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool.