Absence of a Vainshtein radius in torsion bigravity
Abstract
It was pointed out long ago by Vainshtein [Phys. Lett. 39B, 393 (1972)] that the weak-field perturbation expansion of generic theories (of the nonlinear Fierz-Pauli type) involving massive spin-2 excitations breaks down below a certain distance around a material source ("Vainshtein radius"), scaling as some inverse power of the spin-2 mass m2, i.e., some positive power of the range m2-1. Here we prove that this conclusion does not apply in a generalized Einstein-Cartan theory (called "torsion bigravity") whose spectrum is made (like that of bimetric gravity) of a massless spin-2 excitation and a massive spin-2 one. Working within a static spherically symmetric ansatz, we prove, by reformulating the field equations in terms of new variables, that one can construct an all-order weak-field perturbative expansion where no denominators involving m2 ever appear in the region r m2-1. In particular, we show how the formal large-range limit, m2 0, leads to a well-defined, finite perturbation expansion, whose all-order structure is discussed in some detail.