Spherically Symmetric Solutions in a New Braneworld Massive Gravity Theory

In this paper, a combination of the braneworld scenario and covariant de Rham-Gabadadze-Tolley (dRGT) massive Gravity theory is proposed. In this setup, the five-dimensional bulk graviton is considered to be massive. The five dimensional nonlinear ghost-free massive gravity theory affects the 3-brane dynamics and the gravitational potential on the brane. Following the solutions with spherical symmetry on the brane, the full field equations together with the generalized Israel-Darmois junction conditions on the brane and their weak field limits are presented in details. Generally, the theory has four Stuckelberg fields along with the components of physical metric. Although analytical solutions of these equations are impossible in general, by considering some simplifying assumptions, two classes of four-dimensional spherically symmetric solutions on the brane with different background Stuckelberg fields are obtained.