Circular Geodesics, Paczyński-Witta Potential and QNMs in the Eikonal Limit for Ayón-Beato-García Black Hole

Parthapratim Pradhan

doi:10.3390/universe4030055

Abstract

We investigate the comprehensive geodesic structure of a spherically symmetric, static charged regular Ayón-Beato and García black hole (BH). We derive the equation of innermost stable circular orbit (ISCO), marginally bound circular orbit (MBCO) and circular photon orbit (CPO) of said BH, which are most relevant to BH accretion disk theory. Using time-like geodesic properties, we derive Paczyński-Witta potential form for this BH which are very relevant to determine the general relativistic effects on the accretion disk. We show that at a certain radius (For example in case of Reissner-Nordstrøm (RN) BH, r ∗ = Q 2 M ), there exists zero angular momentum (ZAM) orbits due to the repulsive gravity. We also show that in the eikonal approximation, the real and imaginary parts of the quasi normal modes (QNM) of the regular BHs can be expressed as in terms of the frequency of the BH and the instability time scale of the unstable null circular geodesics. Moreover, we study the Bañados, Silk and West effect for this BH. We show that the center-of-mass (CM) energy of colliding neutral test particles near the infinite red-shift surface of the regular BHs have the finite energy. In the Appendix section, we have discussed the possibility of a regular ABG BH can act as particle accelerators when two charged test particles of different energies are colliding and approaching to the horizon of the BH provided that one of charged test particle has a critical value of charge.

Highlights

Geodesic motion of test particles for various BHs spacetime namelySchwarzschild BH, RN BH, Kerr BH, Kerr-Newman BH have been studied by various authors in different way [1,2,3,4,5,6,7]
We show that the center-of-mass (CM) energy of colliding neutral test particles near the infinite red-shift surface of the regular BHs have the finite energy
We compute the QNM frequency for spherically symmetric ABG BH in the eikonal limit using the concept of Lyapunov exponent. It has been shown by Cardoso et al [31] that there is a valid relation between null circular geodesics and QNM in the eikonal limit

Summary

Introduction

Geodesic motion of test particles (both timelike and lightlike) for various BHs spacetime namely. In this work, we have studied the complete geodesic structure of neutral test particle motion of a regular Ayón-Beato and García BH. Paczyński-Witta potential could be used to describe the general relativistic effects on the accretion disk properties That this potential could help us to determine the approximate solutions of the hydrodynamical equations. In [28], the authors considered the geodesic properties for ABG BH and Bardeen BH by using the features of no-horizon structure of the BHs. From the author’s best of knowledge, previously pseudo-Newtonian potential & QNM frequency for regular ABG BH in the eikonal limit have not been considered in the literature.

Equatorial Circular Orbits in ABG Space-Time

Photon Orbits

Null Circular Geodesics and QNM for ABG Spacetime in the Eikonal Limit

Summary and Conclusions