Mass parameter and the bounds on redshifts and blueshifts of photons emitted from geodesic particle orbiting in the vicinity of regular black holes

TL;DR

This paper derives the mass parameter of certain regular black holes using photon redshift and blueshift measurements from orbiting particles, accounting for nonlinear electrodynamics effects on photon trajectories.

Contribution

It introduces a method to determine black hole mass parameters from photon shifts, considering nonlinear electrodynamics influences on photon paths, which is a novel approach.

Findings

Derived bounds on photon redshift and blueshift for regular black holes.

Established relationships between photon shifts and black hole observables.

Numerically analyzed photon shift bounds for specific regular black holes.

Abstract

We obtain the mass parameter for a class of static and spherically symmetric regular black holes (BHs) (namely Bardeen, Hayward and Ay\'{o}n-Beato-Garc\'{i}a BHs) which are solutions of Einstein's field equations coupled to nonlinear electrodynamics (NED) in terms of redshifts and blueshifts of photons emitted by geodesic particles (for instance, stars) orbiting around these BHs. The motion of photons is not governed by null geodesics for these type of spacetime geometries which reflects the direct effects of the electrodynamic nonlinearities in the photon motion; hence, an effective geometry needs to be constructed to study null trajectories [Phys. Rev. D61, 045001 (2000)]. To achieve the above, we first study the constants of motion from the analysis of the motion of both geodesic particles moving in stable circular orbits and photons ejected from them and reaching a distant observer (or detector) in the equatorial plane for the above mentioned regular BHs. The relationship between red/blueshifts of photons and the regular BH observables is presented. We also numerically find the bounds on the photon shifts for these regular BH cases.