Observational redshift from general spherically symmetric black holes

TL;DR

This paper derives a general expression for the observational redshift of photons emitted by particles orbiting spherically symmetric black holes, applying it to a nonsingular black hole model and analyzing parameter effects.

Contribution

It provides a new formalism for calculating redshift in general spherically symmetric black holes and relates black hole parameters to observable redshift in a specific nonsingular black hole model.

Findings

Derived a general redshift expression in terms of metric components.

Applied the formalism to a nonsingular black hole with additional parameters.

Compared redshift effects between nonsingular and Schwarzschild black holes.

Abstract

In this work, we obtain an expression for the total observational frequency shift of photons emitted by massive geodesic particles circularly orbiting a black hole in a general spherically symmetric background. Our general relations are presented in terms of the metric components and their derivatives that characterize the black hole parameters. As a concrete example of this general relativistic approach, a special case is studied by applying the formalism to a nonsingular black hole conformally related to the Schwarzchild solution that possesses a length scale parameter $l$ and an integer parameter $N$ in addition to the black hole mass. Besides, we express the nonsingular black hole mass in terms of the observational redshift/blueshift. Finally, we investigate the effects of the free parameters of the conformal gravity theory on the observational frequency shift and compare results with those of the standard Schwarzschild black hole.