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

TL;DR

This paper derives explicit formulas to determine a Kerr black hole's mass and spin using minimal observational data from photons emitted by orbiting stars, simplifying the process of black hole parameter estimation.

Contribution

It provides new closed-form formulas linking black hole parameters to observable redshifts and orbital radii, requiring fewer measurements than previous methods.

Findings

Formulas for mass and spin from redshift and orbital data

Applicable to systems with one, two, or three orbiting stars

Reduces observational requirements for black hole characterization

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.