Analytical time-like geodesics in modified Hayward black hole space-time

TL;DR

This paper analyzes particle geodesics in modified Hayward black hole space-time, revealing how parameters influence orbit types, and finds that modifications affect the innermost stable circular orbit and angular momentum.

Contribution

It provides a detailed analysis of geodesic orbits in modified Hayward black holes, incorporating quantum corrections and time delay effects, which is a novel extension over previous models.

Findings

No escape orbits for certain parameter ranges.

Modified terms increase the ISCO radius and angular momentum.

Orbital properties depend on parameters b, α, and β.

Abstract

The properties of modified Hayward black hole space-time can be investigated through analyzing the particle geodesics. By means of a detailed analysis of the corresponding effective potentials for a massive particle, we find all possible orbits which are allowed by the energy levels. The trajectories of orbits are plotted by solving the equation of orbital motion numerically. We conclude that whether there is an escape orbit is associated with $b$ (angular momentum). The properties of orbital motion are related to $b$, $\alpha$ ($\alpha$ is associated with the time delay) and $\beta$ ($\beta$ is related to 1-loop quantum corrections). There are no escape orbits when $b$ $<$ $4.016M$, $\alpha$ = 0.50 and $\beta$ = 1.00. For fixed $\alpha$ = 0.50 and $\beta$ = 1.00, if $b$ $<$ $3.493M$, there only exist unstable orbits. Comparing with the regular Hayward black hole, we go for a reasonable speculation by mean of the existing calculating results that the introduction of the modified term makes the radius of the innermost circular orbit (ISCO) and the corresponding angular momentum larger.