Restoring General Relativity in massive bi-gravity theory
arXiv:1307.3640 · doi:10.1103/PhysRevD.88.084002
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.
18 pages, 10 figures, typos corrected, version published in PRD
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