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We construct from first principles a general relativistic approach to studySchwarzschild black hole (BH) rotation curves and estimate the mass-to-distanceratio of the active galactic nucleus of NGC 4258 in terms of astrophysicalobservable quantities. The presented method allows one to clearly distinguishand quantify the general and special relativistic contributions to the totalredshift expression. The total relativistic redshift/blueshift comprises threecomponents: the gravitational redshift due to the spacetime curvature generatedby the mass of the BH in its vicinity, the kinematic shift, originated by thephotons' local Doppler effect, and the redshift due to a special relativisticboost that describes the motion of a galaxy from a distant observer. We applyour method to the largest data set of highly redshifted water megamasermeasurements on the accretion disk of the NGC 4258 active galaxy and use thisgeneral relativistic method to estimate its BH mass-to-distance ratio: M/D =(0.5326 +/- 0.00022) x 10^7 solar masses/Mpc.

Toward the Gravitational Redshift Detection in NGC 4258 and the Estimation of its Black Hole Mass-to-Distance Ratio