Spherically symmetric spacetimes in massive gravity

TL;DR

This paper investigates spherically symmetric solutions in massive gravity, challenging claims of non-linear effects curing linear discontinuities, and finds most solutions develop singularities, but identifies special solutions with promising phenomenological features.

Contribution

It critically examines the resummation approach to resolve the vDVZ discontinuity and introduces a class of solutions with spontaneous symmetry breaking that align with general relativity near sources.

Findings

Linearized theory discontinuity is not robust under modifications.

Most solutions become singular at finite radius for small graviton mass.

A special class of solutions exhibits near-GR behavior and de Sitter asymptotics.

Abstract

We explore spherically symmetric stationary solutions, generated by ``stars'' with regular interiors, in purely massive gravity. We reexamine the claim that the resummation of non-linear effects can cure, in a domain near the source, the discontinuity exhibited by the linearized theory as the mass m of the graviton tends to zero. First, we find analytical difficulties with this claim, which appears not to be robust under slight changes in the form of the mass term. Second, by numerically exploring the inward continuation of the class of asymptotically flat solutions, we find that, when m is ``small'', they all end up in a singularity at a finite radius, well outside the source, instead of joining some conjectured ``continuous'' solution near the source. We reopen, however, the possibility of reconciling massive gravity with phenomenology by exhibiting a special class of solutions, with ``spontaneous symmetry breaking'' features, which are close, near the source, to general relativistic solutions and asymptote, for large radii, a de Sitter solution of curvature ~m^2.