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In this work, we elaborate on the development of a general relativisticformalism that allows one to analytically express the mass and spin parametersof the Kerr black hole in terms of observational data: the total redshift andblueshift of photons emitted by geodesic massive particles revolving the blackhole and their orbital parameters. Thus, we present concise closed formulas forthe mass and spin parameters of the Kerr black hole in terms of few directlyobserved quantities in the case of equatorial circular orbits either when theblack hole is static or is moving with respect to a distant observer.Furthermore, we incorporate the gravitational dragging effect generated by therotating nature of the Kerr black hole into the analysis and elucidate itsnon-trivial contribution to the expression for the light bending parameter andthe frequency shifts of photons emitted by orbiting particles that renderssimple symmetric expressions for the kinematic redshift and blueshift. We alsoincorporate the dependency of the frequency shift on the azimuthal angle, afact that allows one to express the total redshift/blueshift along any point ofthe orbit of the revolving particle for the cases when the black hole is bothstatic or moving with respect to us. These formulas allow one to compute theKerr black hole parameters by applying this general relativistic formalism toastrophysical systems like the megamaser accretion disks orbiting supermassiveblack holes at the core of active galactic nuclei. Our results open a newwindow to implement parameter estimation studies to constrain black holevariables, and they can be generalized to black hole solutions beyond Einsteingravity.

Mass and spin of Kerr black holes in terms of observational quantities: The dragging effect on the redshift