Spherically symmetric spacetimes in massive gravity

TL;DR

Damour, Kogan, and Papazoglou critically assess spherically symmetric solutions in purely massive gravity, testing the Vainshtein continuity idea. Through analytic perturbation theory and detailed gauge formulations, they show that asymptotically flat solutions typically become singular at finite radii as m → 0, challenging the hope that nonlinearities heal the linear discontinuity with GR. They find a special symmetry-breaking class of solutions that are GR-like near sources but possess de Sitter asymptotics at large distances, contingent on the choice of mass term and the presence of a Stueckelberg-like link, offering a potential phenomenological path while highlighting unresolved stability and global-structure issues. Overall, their results argue against a generic, globally smooth massless limit for massive gravity and point to symmetry-breaking, cosmological-tail solutions as a promising but delicate alternative requiring further theoretical and observational scrutiny.

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.