Characterising Vainshtein Solutions in Massive Gravity

TL;DR

This paper analyzes static, spherically symmetric solutions in a ghost-free non-linear massive gravity model, focusing on the Vainshtein mechanism, solution properties, and parameter space regions where solutions exist or fail.

Contribution

It provides an analytical characterization of solution types, their matching conditions, and the conditions under which the Vainshtein mechanism operates in this gravity model.

Findings

Existence of asymptotically flat and non-flat solutions.

Identification of solutions exhibiting the Vainshtein mechanism.

Regions in parameter space where global solutions do not exist.

Abstract

We study static, spherically symmetric solutions in a recently proposed ghost-free model of non-linear massive gravity. We focus on a branch of solutions where the helicity-0 mode can be strongly coupled within certain radial regions, giving rise to the Vainshtein effect. We truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all non-linearities of the helicity-0 mode. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. We find two kinds of asymptotic solutions, one of which is asymptotically flat, while the other one is not, and also two types of inner solutions, one of which displays the Vainshtein mechanism, while the other exhibits a self-shielding behaviour of the gravitational field. We analyse in detail in which cases the solutions match in an intermediate region. The asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while the non asymptotically flat solutions can connect with both kinds of inner solutions. We show furthermore that there are some regions in the parameter space where global solutions do not exist, and characterise precisely in which regions of the phase space the Vainshtein mechanism takes place.