https://doi.org/10.1140/epjc/s10052-026-15510-9
Regular Article - Theoretical Physics
The bound orbits and gravitational waveforms of timelike particles around renormalization group improved Kerr black holes
1
School of Science, Jiangsu University of Science and Technology, 212100, Zhenjiang, China
2
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
a
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Received:
20
September
2025
Accepted:
1
March
2026
Published online:
12
March
2026
Abstract
In this article, we investigate the bound orbits of the timelike particles and the gravitational waveforms emitted from these orbits around a renormalization group improved Kerr black hole in the framework of the asymptotic safety approach. The running Newton coupling in the metric is characterized by two free quantum parameters 
arising from the non-perturbative renormalization group theory and the appropriate cutoff identification, respectively. As expected, the radii of the horizon, the marginally bound orbits and the innermost stable orbit are all decrease as the quantum parameters increase. Under the extreme mass-ratio inspirals approximation the deviation of gravitational waveforms radiated by the periodic orbits from those in the classical Kerr background increases with the two quantum parameters. However, this effect is much smaller in the retrograde case compared to the prograde case. Especially, by comparing the characteristic strain of those gravitational wave with the sensitivity curve of several potential detectors, we find that their characteristic frequencies can fall within the sensitivity ranges of several planned gravitational wave observatories, suggesting that such signals may be detectable with sufficient instrumental sensitivity.
© The Author(s) 2026
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