General Relativistic Formulas For Mass And Spin Of A Kerr Black Hole In Terms Of Redshifts And Orbital Parameters

We derive closed formulas for the mass M and spin a 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 for a single star orbiting the black hole, we need a minimal set of four observational measurements to analytically determine both parameters. Indeed, given a set of two (three) stars revolving around the black hole, these formulas involve just eight (twelve) observational data.