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In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angularmomentum and the charge of the Kerr black hole solution in thescalar-tensor-vector gravity theory [known as the Kerr-MOG (modified-gravity)black hole configuration]; we study in detail as well several properties ofthis solution such as the stationary limit surface, the event horizon, and theergosphere, and conclude that the new deformation parameter $\alpha$ affectsthe geometry of the Kerr-MOG black hole significantly in addition to the ADMmass and spin parameters. Moreover, the ADM mass and black hole event horizondefinitions allow us to set a novel upper bound on the deformation parameterand to reveal the correct upper bound on the black hole spin. We further findthe geodesics of motion of stars and photons around the Kerr-MOG black hole. Byusing them we reveal the expressions for the mass and the rotation parameter ofthe Kerr-MOG black hole in terms of the red- and blueshifts of photons emittedby geodesic particles, i.e., by stars. These calculations supply a new andsimple method to further test the general theory of relativity in its strongfield limit: If the measured red- and blueshifts of photons exceed the boundsimposed by the general theory of relativity, then the black hole is not of Kerrtype. It could also happen that the measurements are allowed by the Kerr-MOGmetric, implying that the correct description of the dynamics of stars around agiven black hole should be performed using MOG or another modified theory ofgravity that correctly predicts the observations. In particular, this methodcan be applied to test the nature of the putative black hole hosted at thecenter of the Milky Way in the near future.

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