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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.

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