Hairy black holes in the ghost-free bigravity theory

Abstract

We study black holes in the recently proposed ghost-free theory with two gravitons, one of which is massive and another is massless. These black holes possess a regular event horizon which is common for both metrics and has the same values of the surface gravity and Hawking temperature with respect to each metric. 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 can be viewed as black hole remnants in the limit where the event horizon shrinks. Finally, adding a matter source we obtain globally regular and asymptotically flat solutions exhibiting the Vainstein mechanism of recovery of General Relativity in a finite region.