Quasilinear static solutions in massive gravity

The static vacuum spherically symmetric solutions of massive gravity theories possess two integration constants: the mass M and a scalar charge S. The presence of this scalar charge reflects the modification of the gravitational interaction as compared to general relativity. Surprisingly, these solutions have an asymptotic behavior different from that obtained in the linear perturbation theory. The aim of this paper is to understand how these modified spherically symmetric solutions emerge from a quasilinear approximation in order to generalize them to any arbitrary mass distribution. Along with these modified solutions, we found a new class of static solutions having a Yukawa shape.