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 St\"{ u}ckelberg fields $\phi^a$, there is new invariant $I^{ ab}=g^{ \mu\nu}\partial_{ \mu}\phi^a\partial_\nu\phi^b$ in the massive gravity, which adds to the ones usually encountered in general relativity (GR). In the unitary gauge $\phi^a=x^\mu\delta_\mu^a$, any inverse metric $g^{ \mu\nu}$ that has divergence including the coordinate singularity in GR would exhibit a singularity in the invariant $I^{ ab}$. 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-Nordstr\"{ o}m solution and five other solutions. These solutions may possess an event horizon depending upon the physical parameters (Schwarzschild radius $r_s$, scalar charge $S$ and/or electric charge $Q$). If these solutions possess an event horizon, we show that the singularity of $I^{ ab}$ is absent at the horizon. Therefore, these solutions may become candidates for black holes in dRGT.
Categories: gr-qc astro-ph.CO hep-th
