Particle motions and gravitational waveforms in rotating black hole spacetimes of loop quantum gravity
We study the influence of the loop quantum gravity (LQG) holonomy-correction parameter $ξ$ on black hole horizon structure, timelike geodesic motion, and gravitational wave emission in two rotating LQG-inspired black hole spacetimes, constructed via Newman-Janis algorithm from two distinct spherically symmetric seed metrics (type BH-I and BH-II). The physically admissible range of $ξ$ is determined by requiring the existence of event horizons, marginally bound orbits, and innermost stable circular orbits simultaneously, and is found to shrink monotonically with increasing spin parameter $a$. For equatorial periodic orbits, increasing $ξ$ at fixed angular momentum enlarges the bound energy range, while for off-equatorial orbits, it suppresses the allowed range of the Carter constant, effectively confining trajectories closer to the equatorial plane. The effects of $ξ$ and $a$ on orbital dynamics are systematically antagonistic. Gravitational waveforms computed within a leading-order post-Newtonian extreme-mass-ratio inspiral (EMRI) model show that larger $ξ$ produces enhanced deviations from the Kerr waveform, more prominently so for type BH-II than type BH-I. The resulting characteristic strains occupy the $(10^{-3}, 0.1)$ Hz frequency band but fall below the sensitivity curves of current and near-future space-based detectors for the EMRI parameters considered ($M=10^7 M_\odot$, $m=10 M_\odot$, $D_L = 200$ Mpc). Adiabatic inspiral calculations confirm that $ξ$ and $a$ drive orbital evolution in opposite directions, with their relative magnitude determining whether quantum corrections accelerate or retard the inspiral. These results establish systematic observational signatures of holonomy corrections in rotating LQG black holes and motivate higher-fidelity waveform modeling for future space-based gravitational wave detectors.