  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.
