Structure of geodesics in the regular Hayward black hole space-time

TL;DR

This paper investigates the structure of geodesics in the regular Hayward black hole spacetime, revealing four types of time-like orbits and three types of null orbits through numerical analysis of effective potentials.

Contribution

It provides a detailed numerical analysis of time-like and null geodesics in the regular Hayward black hole spacetime, identifying orbit types and their dependence on parameters.

Findings

Four types of time-like orbits identified: planetary, circular, escape, absorbing.

Null geodesics have three orbit types: unstable circle, escape, absorbing.

Orbit structures depend on parameters like energy density and angular momentum.

Abstract

The regular Hayward model describes a non-singular black hole space-time. By analyzing the behaviors of effective potential and solving the equation of orbital motion, we investigate the time-like and null geodesics in the regular Hayward black hole space-time. Through detailed analyses of corresponding effective potentials for massive particles and photons, all possible orbits are numerically simulated. The results show that there may exist four orbital types in the time-like geodesics structure: planetary orbits, circular orbits, escape orbits and absorbing orbits. In addition, when $\ell$, a convenient encoding of the central energy density $3/8\pi\ell^{2}$, is $0.6M$, and $b$ is $3.9512M$ as a specific value of angular momentum, escape orbits exist only under $b>3.9512M$. The precession direction is also associated with values of $b$. With $b=3.70M$ the bound orbits shift clockwise but counter-clockwise with $b=5.00M$ in the regular Hayward black hole space-time. We also find that the structure of null geodesics is simpler than that of time-like geodesics. There only exist three kinds of orbits (unstable circle orbits, escape orbits and absorbing orbits).