Mass and spin of a Kerr black hole in modified gravity and a test of the Kerr black hole hypothesis

TL;DR

This paper investigates the properties of Kerr black holes within a modified gravity framework, deriving mass, spin, and observational signatures to test the Kerr hypothesis against alternative theories.

Contribution

It introduces a detailed analysis of Kerr-MOG black holes, including new bounds on deformation parameters and a novel method using photon red- and blueshifts to test gravity theories.

Findings

Derived ADM mass, angular momentum, and charge for Kerr-MOG black holes.

Established upper bounds on the deformation parameter and black hole spin.

Proposed a new observational method to distinguish Kerr black holes from modified gravity scenarios.

Abstract

In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angular momentum and the charge of the Kerr black hole solution in the scalar-tensor-vector gravity theory [known as the Kerr-MOG (modified-gravity) black hole configuration]; we study in detail as well several properties of this solution such as the stationary limit surface, the event horizon, and the ergosphere, and conclude that the new deformation parameter $\alpha$ affects the geometry of the Kerr-MOG black hole significantly in addition to the ADM mass and spin parameters. Moreover, the ADM mass and black hole event horizon definitions allow us to set a novel upper bound on the deformation parameter and to reveal the correct upper bound on the black hole spin. We further find the geodesics of motion of stars and photons around the Kerr-MOG black hole. By using them we reveal the expressions for the mass and the rotation parameter of the Kerr-MOG black hole in terms of the red- and blueshifts of photons emitted by geodesic particles, i.e., by stars. These calculations supply a new and simple method to further test the general theory of relativity in its strong field limit: If the measured red- and blueshifts of photons exceed the bounds imposed by the general theory of relativity, then the black hole is not of Kerr type. It could also happen that the measurements are allowed by the Kerr-MOG metric, implying that the correct description of the dynamics of stars around a given black hole should be performed using MOG or another modified theory of gravity that correctly predicts the observations. In particular, this method can be applied to test the nature of the putative black hole hosted at the center of the Milky Way in the near future.