Signatures of Quantum-Corrected Black Holes in Gravitational Waves from Periodic Orbits

Abstract: We investigate gravitational wave emission from periodic timelike orbits of a test particle around a loop quantum gravity-inspired Schwarzschild black hole. The spacetime is characterised by a holonomy-correction parameter that modifies the radial metric component while preserving asymptotic flatness and the classical location of the horizon. The bound geodesics are systematically classified using the zoom--whirl representation labelled by three integers $(z,w,v)$. Gravitational waveforms are computed within a numerical framework that combines exact geodesic motion with the quadrupole approximation, which is suitable for extreme mass ratio inspirals. We demonstrate that the quantum corrections lead to distinct phase shifts, amplitude variations, and modifications to the harmonic structure of the waveforms, with increasingly complex features for orbits with larger zoom numbers. The corresponding frequency spectra and characteristic strain peak, which fall within the millihertz band, are within the sensitivity ranges of space-based detectors such as LISA, Taiji, and TianQin. For specific orbital configurations and values of the quantum-correction parameter, the characteristic strain exceeds the projected detector noise, indicating potential observability. Our results demonstrate that gravitational waves from periodic orbits provide a sensitive probe of quantum-corrected black hole spacetimes in the strong-field regime.