General relativistic formulas for mass and spin of a Kerr black hole in terms of redshifts and orbital parameters

Abstract

We derive closed formulas for the mass and spin parameters of a Kerr black hole in terms of a minimal quantity of observational data: the red-/blue-shifts of photons emitted by massive particles (stars) moving on geodesics around the black hole and their respective orbital radius. It turns out that given a set of two (three) stars revolving around the black hole, these formulas involve just eight (twelve) observational data. For the case of a single star orbiting the black hole we need a minimal set of four observational measurements to analytically determine both parameters.