Quasi-linear static solutions in massive gravity

TL;DR

This paper investigates static spherically symmetric solutions in massive gravity, revealing non-linear behaviors at large distances and introducing a quasi-linear approximation to understand these modifications beyond linear theory.

Contribution

It introduces a quasi-linear approach to derive modified spherically symmetric solutions in massive gravity, including a new class with Yukawa potential shapes.

Findings

Solutions exhibit non-linear behavior at large distances.

Existence of a scalar charge modifies gravitational interactions.

Discovery of a new Yukawa-shaped static solution.

Abstract

The static vacuum spherically symmetric solutions of massive gravity theories possess two integration constant: the mass M and a scalar charge S. The presence of this scalar charge reflects the modification of the gravitational interaction as compared to General Relativity. Surprisingly, these solutions are non-linear even at large distances from the sources, implying that their asymptotic behavior is different from that obtained in the linear perturbation theory. The aim of this paper is to understand how these modified spherically symmetric solutions emerge from a quasi-linear approximation in order to generalize them to any arbitrary mass distribution. Along with these modified solutions, we found a new class of static solutions having a Yukawa shape.