Toward the Gravitational Redshift Detection in NGC 4258 and the
  Estimation of its Black Hole Mass-to-Distance Ratio
  We construct from first principles a general relativistic approach to study
Schwarzschild black hole (BH) rotation curves and estimate the mass-to-distance
ratio of the active galactic nucleus of NGC 4258 in terms of astrophysical
observable quantities. The presented method allows one to clearly distinguish
and quantify the general and special relativistic contributions to the total
redshift expression. The total relativistic redshift/blueshift comprises three
components: the gravitational redshift due to the spacetime curvature generated
by the mass of the BH in its vicinity, the kinematic shift, originated by the
photons' local Doppler effect, and the redshift due to a special relativistic
boost that describes the motion of a galaxy from a distant observer. We apply
our method to the largest data set of highly redshifted water megamaser
measurements on the accretion disk of the NGC 4258 active galaxy and use this
general relativistic method to estimate its BH mass-to-distance ratio: M/D =
(0.5326 +/- 0.00022) x 10^7 solar masses/Mpc.
