Null Geodesics and QNMs in the field of Regular Black Holes

TL;DR

This paper investigates null and time-like geodesics in regular black holes, exploring photon spheres, shadows, light bending, and their relation to quasinormal modes, with implications for black hole stability and accretion disk physics.

Contribution

It provides a comprehensive analysis of geodesic structures, shadow formation, and QNM relations in regular black holes, including effects of various parameters and scalar perturbations.

Findings

Photon sphere radius and shadow size depend on black hole parameters.

QNMs in the eikonal limit are governed by null geodesics, linking stability and oscillation frequencies.

Massless and massive scalar perturbations exhibit characteristic effective potentials.

Abstract

We analyze the null geodesics of regular black holes. A detailed analysis of geodesic structure both null geodesics and time-like geodesics have been investigated for the said black hole. As an application of null geodecics, we calculate the radius of photon sphere and gravitational bending of light. We also study the shadow of the black hole spacetime. Moreover, we determine the relation between radius of photon sphere~$(r_{ps})$ and the shadow observed by a distance observer. Furthermore, We discus the effect of various parameters on the radius of shadow $R_s$. Also we compute the angle of deflection for the photons as a physical application of null-circular geodesics. We find the relation between null geodesics and quasinormal modes frequency in the eikonal approximation by computing the Lyapunov exponent. It is also shown that~(in the eikonal limit) the quasinormal modes~(QNMs) of black holes are governed by the parameter of null-circular geodesics. The real part of QNMs frequency determines the angular frequency whereas the imaginary part determines the instability time scale of the circular orbit. Next we study the massless scalar perturbations and analyze the effective potential graphically. Massive scalar perturbations also discussed. As an application of time-like geodesics we compute the innermost stable circular orbit~(ISCO) and marginally bound circular orbit~(MBCO) of the regular BHs which are closely related to the black hole accretion disk theory. In the appendix, we calculate the relation between angular frequency and Lyapunov exponent for null-circular geodesics.