Restoring General Relativity in massive bi-gravity theory

TL;DR

This paper demonstrates how massive bi-gravity theory can recover General Relativity within the Vainshtein radius, providing analytic solutions that interpolate between GR and flat spacetime, and explores the mathematical structure of these solutions.

Contribution

It shows the recovery of General Relativity in massive bi-gravity via the Vainshtein mechanism and derives a polynomial equation governing the solutions.

Findings

General Relativity is recovered within the Vainshtein radius.

A seventh-order polynomial equation determines the solutions.

Solutions are analytic in regimes below and beyond the Vainshtein radius.

Abstract

We study static spherically symmetric solutions of massive bi-gravity theory, free from the Boulware-Deser ghost. We show the recovery of General Relativity via the Vainshtein mechanism, in the weak limit of the physical metric. We find a single polynomial equation determining the behavior of the solution for distances smaller than the inverse graviton mass. This equation is generically of the seventh order, while for a specific choice of the parameters of the theory it can be reduced to lower orders. The solution is analytic in different regimes: for distances below the Vainshtein radius (where General Relativity is recovered), and in the opposite regime, beyond the Vainshtein radius, where the solution approaches the flat metric.