Quantum Corrected Geodesic Motion in Polymer Kerr-like Spacetime

TL;DR

This work explores how quantum gravity effects in a polymerized loop-quantum-gravity framework modify timelike geodesics around a Kerr-like black hole. By deriving the radial potential and analyzing circular and marginal orbits, the authors show that increasing the quantum parameter $A_\lambda$ lowers the radii, energy, and angular momentum of ISCOs and MCOs, with prograde orbits exhibiting greater sensitivity. The study also analyzes periodic orbits through a rational-number structure, finding that $A_\lambda$ shifts root structures, reduces eccentricity of bound motion, and alters the energy-angular-momentum balance for fixed orbital topologies. These results suggest observable imprints in EMRI signals and offer a pathway to test quantum-gravity corrections with future gravitational-wave measurements, especially in strong-field regimes near wormhole transitions.

Abstract

Rotating black holes are prevalent in astrophysical observations, and a Kerr-like solution that incorporates quantum gravity effects is essential for constructing realistic models. In this work, we analyze the geodesic motion of massive particles in a Kerr-like polymer spacetime, incorporating quantum corrections via a parameter $A_λ$. We demonstrate that increasing $A_λ$ allows for additional orbital evolution in extreme mass ratio inspiral (EMRI) systems before merging. Our results show that the radii, energy, and angular momentum of both the innermost stable circular orbit (ISCO) and marginal circular orbit (MCO) decrease as $A_λ$ increases. Furthermore, when the primary object becomes a wormhole, both prograde ISCO and MCO can intersect the transition surface at the wormhole throat and vanish as $A_λ$ grows. Additionally, we find that the eccentricity of periodic geodesic motion decreases monotonically with increasing $A_λ$. Finally, we explore the variation of the rational number that characterizes periodic motion and highlight the influence of the quantum parameter on different types of periodic orbits, classified by a set of integers associated with the rational number. This work contributes to the understanding of quantum gravity effects and offers potential observational signatures, particularly in the study of EMRIs.

Figures (10)

• Figure 1: The spacetime structure of the black hole determined by the parameter space $(a, A_\lambda)$, the red line represents the transition surface located on the outer horizon, the blue line represents the transition surface located on the inner horizon.
• Figure 2: The radial potential for a massive test particle around a rotating LQG polymer black hole for different values of $A_\lambda$. Parameters are fixed at $E = 0.95$, $a = 0.5$, and $L = 3$.
• Figure 3: Allowed parameter space for orbital angular momentum and energy of bound orbits for different values of $A_\lambda$. (a): the prograde motion, (b): the retrograde motion.
• Figure 4: (a) and (c): MCO radius and angular momentum as functions of $A_\lambda$ for prograde orbits. (b) and (d): MCO for retrograde orbits. The dashed line represents the position of the transition surface.
• Figure 5: The position, angular momentum, and energy of prograde ISCO (left) and retrograde ISCO (right) as functions of $A_\lambda$ with different values of $a$.