The recovery of General Relativity in massive gravity via the Vainshtein mechanism

TL;DR

This paper investigates how non-linear massive gravity models recover General Relativity at small scales through the Vainshtein mechanism, using numerical and analytical methods to analyze spherically symmetric solutions.

Contribution

It provides detailed numerical solutions and new analytical insights into the Vainshtein mechanism in non-linear massive gravity theories.

Findings

Recovery of GR solutions via Vainshtein mechanism demonstrated

Analytic understanding of solution behavior at infinity

Weak field limit captures key features of the numerical solutions

Abstract

We study in detail static spherically symmetric solutions of non linear Pauli-Fierz theory. We obtain a numerical solution with a constant density source. This solution shows a recovery of the corresponding solution of General Relativity via the Vainshtein mechanism. This result has already been presented by us in a recent letter, and we give here more detailed information on it as well as on the procedure used to obtain it. We give new analytic insights upon this problem, in particular for what concerns the question of the number of solutions at infinity. We also present a weak field limit which allows to capture all the salient features of the numerical solution, including the Vainshtein crossover and the Yukawa decay.