# Null Geodesics and QNMs of Regular Black Holes in AdS space

Research paper by Monimala Mondal, Anil Kumar Yadav, Parthapratim Pradhan, Sayeedul Islam, Farook Rahaman

Indexed on: 08 Sep '20Published on: 03 Sep '20Published in: arXiv - General Relativity and Quantum Cosmology

#### Abstract

We analyze the null geodesics of regular black holes in AdS space. 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 calculte 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 in AdS space-time 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.