Black holes in torsion bigravity

Abstract

We study spherically symmetric black hole solutions in a four-parameter Einstein-Cartan-type class of theories, called "torsion bigravity". These theories offer a geometric framework (with a metric and an independent torsionfull connection) for a modification of Einstein's theory that has the same spectrum as bimetric gravity models. In addition to an Einsteinlike massless spin-2 excitation, there is a massive spin-2 one (of range $\kappa^{-1}$) coming from the torsion sector, rather than from a second metric. We prove the existence of three broad classes of spherically-symmetric black hole solutions in torsion bigravity. First, the Schwarzschild solution defines an asymptotically-flat torsionless black hole for all values of the parameters. [And we prove that one cannot deform a Schwarzschild solution, at the linearized level, by adding an infinitesimal torsion hair.] Second, when considering finite values of the range, we find that there exist non-asymptotically-flat torsion-hairy black holes in a large domain of parameter space. Third, we find that, in the limit of infinite range, there exists a two-parameter family of asymptotically flat torsion-hairy black holes. The latter black hole solutions give an interesting example of non-Einsteinian (but still purely geometric) black hole structures which might be astrophysically relevant when considering a range of cosmological size.