Black hole solutions in de Rham-Gabadadze-Tolley massive gravity
  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.
