Calculation of the Kerr black hole parameters in terms of its rotation curves
Date
2019-12
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Benemérita Universidad Autónoma de Puebla
Abstract
"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 travel along null geodesics towards a distant observer (located at a finite distance), and ii) the radius of these star 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 the distant observer".