Schwarzschild black hole and redshift rapidity: A new approach towards measuring cosmic distances

TL;DR

This paper introduces the concept of redshift rapidity, a relativistic invariant, to improve the measurement of black hole mass and distance in a fully general relativistic framework, enhancing cosmic distance estimation accuracy.

Contribution

It proposes a novel relativistic invariant called redshift rapidity to disentangle black hole mass and distance using observational data within Schwarzschild spacetime.

Findings

Derived analytic formulas for mass and distance estimation.

Formulas applicable to megamaser systems and black hole studies.

Enhanced precision in cosmic distance measurements.

Abstract

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.