Null geodesics and QNMs in the field of regular black holes

Abstract

In this paper, we analyze the null geodesics of regular black holes (BHs). A detailed analysis of geodesic structure, both null geodesics and timelike geodesics, has been investigated for the said BH. As an application of null geodesics, we calculate the radius of photon sphere and gravitational bending of light. We also study the shadow of the BH spacetime. Moreover, we determine the relation between radius of photon sphere [Formula: see text] and the shadow observed by a distance observer. Furthermore, we discuss the effect of various parameters on the radius of shadow [Formula: see text]. 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 mode (QNM) frequency in the eikonal approximation by computing the Lyapunov exponent. It is also shown that (in the eikonal limit) the QNMs of BHs 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 timescale of the circular orbit. Next, we study the massless scalar perturbations and analyze the effective potential graphically. Massive scalar perturbations are also discussed. As an application of timelike 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 BH accretion disk theory. In the appendix, we calculate the relation between angular frequency and Lyapunov exponent for null-circular geodesics.