  Motivated by recent achievements of a full general relativistic method in
estimating the mass-to-distance ratio of supermassive black holes hosted at the
core of active galactic nuclei, we introduce the new concept redshift rapidity
in order to express the Schwarzschild black hole mass and its distance from the
Earth just in terms of observational quantities. The redshift rapidity is also
an observable relativistic invariant that represents the evolution of the
frequency shift with respect to proper time in the Schwarzschild spacetime. We
extract concise and elegant analytic formulas that allow us to disentangle mass
and distance to black holes in the Schwarzschild background and estimate these
parameters separately. This procedure is performed in a completely general
relativistic way with the aim of improving the precision in measuring cosmic
distances to astrophysical compact objects. Our exact formulas are valid on the
midline and close to the line of sight, having direct astrophysical
applications for megamaser systems, whereas the general relations can be
employed in black hole parameter estimation studies.
