Black hole mass and distance from accretion disk astrophysical observables

TL;DR

This paper derives new analytical formulas to determine black hole mass, distance, and orbital radius from astrophysical observables, incorporating relativistic effects and peculiar motions.

Contribution

It introduces a general relativistic method using frequency shifts and redshift rapidity to analytically estimate black hole parameters from orbiting particle observations.

Findings

Derived formulas for black hole mass and distance from frequency shifts.

Extended formulas to systems with peculiar motion.

Provided analytical expressions for orbital radius of test particles.

Abstract

In this work we derive novel analytical expressions for the mass and distance of a Schwarzschild black hole (BH), as well as for the orbital radius of test particles orbiting it, it terms of astrophysical observables measured throughout the entire orbit of the revolving particle. We use a general relativistic method to describe the frequency shifts of photons emitted in the vivinity of a BH by considering two emitters (or two positions of the same emitter) located symmetrically opposite to each other with respect to the observer's line of sight (LOS) when performing measurements along the orbit. Furthermore, the introduction of the redshift rapidity allows us to write independent expressions for the BH mass and its distance to Earth. We also extend our study to the case when astrophysical systems have a peculiar motion and derive the corresponding closed formulas.