1202.6682 (Mikhail S. Volkov)
Mikhail S. Volkov
We study static, spherically symmetric black holes in the recently proposed massive gravity theory with two dynamical metrics that is maintained to be ghost-free. These solutions possess a regular event horizon common for both metrics, the values of the surface gravity and Hawking temperature calculated with respect to each metric being the same. The ratio of the event horizon radii measured by the two metrics is a free parameter that labels the solutions. We present a numerical evidence for their existence and find that they comprise several classes. Black holes within each class approach the same AdS-type asymptotic at infinity but differ from each other in the event horizon vicinity where the short-range massive modes reside. In addition, there are solutions showing a curvature singularity at a finite proper distance from the horizon. For some special solutions the graviton mass may become effectively imaginary, causing oscillations around the flat metric at infinity. The only asymptotically flat black hole we find -- the Schwarzschild solution obtained by identifying the two metrics -- seems to be exceptional, since changing even slightly its horizon boundary conditions completely changes the asymptotic behavior at infinity. We also construct globally regular solutions describing `lumps of pure gravity' which show the same far field behavior as the black holes. However, adding a matter source gives asymptotically flat solutions exhibiting the Vainstein mechanism of recovery of General Relativity in a finite region.
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http://arxiv.org/abs/1202.6682
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