An infinite class of exact rotating black hole metrics of modified gravity

TL;DR

This paper constructs an infinite class of exact rotating black hole solutions in a modified gravity theory, extending solution methods beyond General Relativity and exploring implications for gravitational phenomenology.

Contribution

It introduces a novel solution-generating method for Ricci-Based Gravity theories, producing explicit rotating black hole metrics including Kerr-Newman analogs.

Findings

Derived axisymmetric solutions for modified gravity theories.

Extended solution methods applicable to various Ricci-Based Gravity models.

Provided explicit Kerr-Newman-like black hole solutions in this framework.

Abstract

We build an infinite class of exact axisymmetric solutions of a metric-affine gravity theory, namely, Eddington-inspired Born-Infeld gravity, coupled to an anisotropic fluid as a matter source. The solution-generating method employed is not unique of this theory but can be extended to other Ricci-Based Gravity theories (RBGs), a class of theories built out of contractions of the Ricci tensor with the metric. This method exploits a correspondence between the space of solutions of General Relativity and that of RBGs, and is independent of the symmetries of the problem. For the particular case in which the fluid is identified with non-linear electromagnetic fields we explicitly derive the corresponding axisymmetric solutions. Finally, we use this result to work out the counterpart of the Kerr-Newman black hole when Maxwell electrodynamics is set on the metric-affine side. Our results open up an exciting new avenue for testing new gravitational phenomenology in the fields of gravitational waves and shadows out of rotating black holes.