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

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.

Compact objects in quadratic Palatini gravity generated by a free scalar field

“…Explicit examples of this correspondence and applications to scenarios with scalar fields, electromagnetic fields, and fluids have been worked out for fðRÞ theories and also for the Born-Infeld gravity model (EiBI) in Refs. [31][32][33][34][35]. It should be noted that this correspondence somehow extends beyond the vacuum case the deep relation already observed in [36,37] between GR and these metric-affine theories.…”

Compact objects in quadratic Palatini gravity generated by a free scalar field

“…Explicit examples of this correspondence and applications to scenarios with scalar fields, electromagnetic fields, and fluids have been worked out for f (R) theories and also for the Born-Infeld gravity model (EiBI) in Refs. [31][32][33][34][35]. It should be noted that this correspondence somehow extends beyond the vacuum case the deep relation already observed in [36,37] between GR and these metric-affine theories.…”

“…[63] or in the analysis of rotating electrovacuum solutions in Refs. [35,64], thus allowing to address complex problems of physical interest in other RBGs beyond the f (R) family. The consideration of other matter sources such as fluids and electromagnetic fields is another important issue which we hope to address in the future.…”

“…( 32) in terms of a modified matter Lagrangian minimally coupled to the metric h µν , removing in that way any reference to the spacetime metric g µν . This method has been used to find various types of solutions in f (R) theories and in the Eddington-inspired Born-Infeld gravity theory [31][32][33][34][35]. In this section, we will focus on implementing the map between GR and f (R, Q) gravity theories in order to facilitate the construction of new solutions in a larger and different family of theories.…”

Some recent results on Ricci-based gravity theories

“…The greatest achievement so far of the correspondence using fluids has been reported in Ref. 49, where an infinite class of axially symmetric rotating solutions has been explicitly constructed for the EiBI theory, though the same logic can be applied to any other RBG. Hopefully, this result will allow to generate a catalogue of new rotating solutions that can be used to confront modified gravity effects with observational data.…”