Spherically symmetric solutions in torsion bigravity

We study spherically symmetric solutions in a four-parameter Einstein-Cartan--type class of theories. These theories include torsion, as well as the metric, as dynamical fields and contain only two physical excitations (around flat spacetime): a massless spin-2 excitation and a massive spin-2 one (of mass m₂≡κ). They offer a geometric framework (which we propose to call ``torsion bigravity'') for a modification of Einstein's theory that has the same spectrum as bimetric gravity models. We find that the spherically symmetric solutions of torsion bigravity theories exhibit several remarkable features: (i) they have the same number of degrees of freedom as their analogs in ghost-free bimetric gravity theories (i.e., one less than in ghostfull bimetric gravity theories); (ii) in the limit of a small mass for the spin-2 field (κ→0), no inverse powers of κ arise at the first two orders of perturbation theory (contrary to what happens in bimetric gravity where 1/κ² factors arise at linear order, and 1/κ⁴ ones at quadratic order). We numerically construct a high-compactness (asymptotically flat) star model in torsion bigravity and show that its geometrical and physical properties are significantly different from those of a general relativistic star having the same observable Keplerian mass.