Vainshtein Mechanism In $\Lambda_3$ - Theories

We explore the space of spherically symmetric, static solutions in the decoupling limit of a class of non-linear covariant extensions of Fierz-Pauli massive gravity obtained recently in arXiv:1007.0443. In general, several such solutions with various asymptotic limits exist. We find their approximate short and long-distance behaviour and use numerical analysis to match them at the Vainshtein radius, $r_*$. Our findings indicate, that for a broad range of parameters, the theory does possess the Vainshtein mechanism, screening the scalar contribution to the gravitational force within $r_*$. In addition, there exists a class of solutions in the literature, for which the $1/r$ gravitational potential is completely screened within the Vainshtein scale. However, numerical analysis indicates, that for this type of solutions, the gravitational potential does not decay at spatial infinity.