Black holes in torsion bigravity

TL;DR

This paper explores black hole solutions in torsion bigravity, a geometric modification of Einstein's theory with additional torsion, revealing new classes of black holes with potential astrophysical relevance.

Contribution

It demonstrates the existence of three classes of spherically symmetric black holes in torsion bigravity, including novel torsion-hairy solutions with varying asymptotic properties.

Findings

Schwarzschild solution is torsionless and cannot be deformed by infinitesimal torsion.

Existence of non-asymptotically-flat torsion-hairy black holes in finite range.

Asymptotically flat torsion-hairy black holes emerge at infinite range.

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.