Slowly rotating black holes in alternative theories of gravity

TL;DR

This paper derives a general analytic solution for slowly rotating black holes in a broad class of alternative gravity theories, providing formulas for orbital frequencies that can test deviations from General Relativity.

Contribution

It presents the first closed-form stationary, slowly rotating black hole solution in alternative theories with quadratic curvature invariants coupled to a scalar field.

Findings

Explicit formulas for orbital frequency changes at ISCO and light ring

Solution as a deformation of Schwarzschild metric

Potential for testing gravity theories with astrophysical observations

Abstract

We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented by all possible quadratic, algebraic curvature invariants coupled to a scalar field. The solution is found as a deformation of the Schwarzschild metric in General Relativity. We explicitly derive the changes to the orbital frequency at the innermost stable circular orbit and at the light ring in closed form. These results could be useful when comparing General Relativity against alternative theories by (say) measurements of X-ray emission in accretion disks, or by stellar motion around supermassive black holes. When gravitational-wave astronomy comes into force, strong constraints on the coupling parameters can in principle be made.