Black holes in the long-range limit of torsion bigravity

We continue the study of spherically symmetric black hole solutions in torsion bigravity, a class of Einstein-Cartan-type gravity theories involving, besides a metric, a massive propagating torsion field. In the infinite-range limit, these theories admit asymptotically flat black hole solutions related to the presence of attractive fixed points in the asymptotic radial evolution of the metric and the torsion. We discuss these fixed points and the way they are approached at large radii. Several phenomenological aspects of asymptotically flat torsion-hairy black holes are discussed: (i) location of the light ring and of the shadow; (ii) correction to the redshift of orbiting stars; and (iii) modification of the periastron precession of orbiting stars. By comparing the observable properties of torsion-hairy black holes to existing observational data on supermassive black holes obtained by the Event Horizon Telescope Collaboration and by the GRAVITY Collaboration, we derive constraints on the theory parameters of torsion bigravity. The strongest constraint is found to come from the recent measurement of the periastron precession of the star S2 orbiting the Galactic-center massive black hole [R. Abuter et al., Astron. Astrophys. 636, L5 (2020) and to be a thousand times more stringent than Solar-System gravitational tests.