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

作者：Li, Ping; Li, Xin-zhou^*; Xi, Ping^*

来源：PHYSICAL REVIEW D, 2016, 93(6): 064040.

DOI：10.1103/PhysRevD.93.064040

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 Stuckelberg fields phi(a), there is new invariant I-ab = g(mu nu)partial derivative(mu)phi(a)partial derivative(nu)phi(b) in the massive gravity, which adds to the ones usually encountered in general relativity (GR). In the unitary gauge phi(a) = chi(mu)delta(a)(mu), 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-Nordstrom 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.

• 出版日期2016-3-16
• 单位上海师范大学