Probing Gravitational Wave Signatures from Periodic Orbits of Regular Black Holes in Asymptotically Safe Gravity

TL;DR

This paper explores how quantum corrections in a regular black hole spacetime affect geodesic motion and gravitational wave signals, with implications for detecting quantum gravity effects via space-based GW observatories.

Contribution

It introduces a detailed analysis of periodic geodesics and GW signatures in a regular black hole model within asymptotically safe gravity, highlighting observable deviations from classical predictions.

Findings

Quantum parameter $\xi$ alters the ISCO and orbital frequencies.

GW signals show amplitude modulations and phase shifts with increasing $\xi$.

Strain spectra are within the sensitivity of LISA, Taiji, and TianQin.

Abstract

We investigate bound and periodic timelike geodesics and their associated gravitational-wave (GW) signatures in the spacetime of a regular black hole arising in asymptotically safe gravity (ASG). The geometry incorporates quantum corrections via a running gravitational coupling, encoded in a dimensional scaling parameter $\xi$, that modifies the near-horizon structure while preserving asymptotic flatness. We derive the effective potential for massive test particles and determine the conditions for stable circular and bound motion as functions of $\xi$, including the shift in the innermost stable circular orbit (ISCO). The three topological integers $(z,w,v)$, which represent the number of zooms, whirls, and vertices per radial cycle, are used to categorize the test particles' periodic orbits using Levin's zoom -- whirl taxonomy. Moreover, we employ the rational frequency ratio $q = \frac{\omega_\phi}{\omega_r} - 1$ to find closed orbits, where $\omega_\phi$ and $\omega_r$ stand for the azimuthal and radial frequencies, respectively. We examine how the orbital frequency spectrum is altered, whirl behaviour is enhanced, and deviations from the Schwarzschild limit are produced by the quantum parameter $\xi$. The GW forms for extreme mass-ratio inspirals (EMRIs) are calculated within the quadrupole approximation. We find that as $\xi$ increases, the signals that are released exhibit detectable amplitude modulations and phase shifts. The corresponding typical strain spectra fall within the anticipated sensitivity limits of space-based detectors such as LISA, Taiji, and TianQin, as they peak in the millihertz frequency band. Peak strain increases monotonically with $\xi$, indicating that observational restrictions on quantum-gravity-induced deviations from classical general relativity in the strong-field domain can be obtained from precise measurements of zoom -- whirl dynamics in EMRIs.