Abstract
We present a detailed study of the static spherically symmetric solutions in de Rham–Gabadadze–Tolley (dRGT) theory. Since the diffeomorphism invariance can be restored by introducing the Stückelberg fields , there is new invariant in the massive gravity, which adds to the ones usually encountered in general relativity (GR). In the unitary gauge , any inverse metric that has divergence including the coordinate singularity in GR would exhibit a singularity in the invariant . Therefore, there is no conventional Schwarzschild metric if we choose unitary gauge. In this paper, we obtain a self-consistent static spherically symmetric ansatz in the nonunitary gauge. Under this ansatz, we find that there are seven solutions including the Schwarzschild solution, Reissner-Nordström solution and five other solutions. These solutions may possess an event horizon depending upon the physical parameters (Schwarzschild radius , scalar charge and/or electric charge ). If these solutions possess an event horizon, we show that the singularity of is absent at the horizon. Therefore, these solutions may become candidates for black holes in dRGT.
- Received 21 January 2016
DOI:https://doi.org/10.1103/PhysRevD.93.064040
© 2016 American Physical Society