Kerr black hole parameters in terms of red/blue shifts of photons
  emitted by geodesic particles
  We are motivated by the recently reported dynamical evidence of stars with
short orbital periods moving around the center of the Milky Way and the
corresponding hypothesis about the existence of a supermassive black hole
hosted at its center. In this paper we show how the mass and rotation
parameters of a Kerr black hole (assuming that the putative supermassive black
hole is of this type), as well as the distance that separates the black hole
from the Earth, can be estimated in a relativistic way in terms of i) the red
and blue shifts of photons that are emitted by geodesic massive particles
(stars and galactic gas) and travel along null geodesics towards a distant
observer, and ii) the radius of these star/gas orbits.
  As a concrete example and as a first step towards a full relativistic
analysis of the above mentioned star orbits around the center of our galaxy, we
consider stable equatorial circular orbits of stars and express their
corresponding red/blue shifts in terms of the metric parameters (mass and
angular momentum per unit mass) and the orbital radii of both the emitter star
(and/or galactic gas) and the distant observer.
  In principle, these expressions allow one to statistically estimate the mass
and rotation parameters of the Kerr black hole, and the radius of our orbit,
through a Bayesian fitting, i.e., with the aid of observational data: the
red/blue shifts measured at certain points of stars' orbits and their radii,
with their respective errors, a task that we hope to perform in the near
future. We also point to several astrophysical phenomena, like accretion discs
of rotating black holes, binary systems and active galactic nuclei, among
others, to which this formalism can be applied.
