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

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 ξ, that modifies the near-horizon structure while preserving asymptotic flatness. Periodic orbits of a stellar-mass compact object around a supermassive black hole are classified using the zoom-whirl taxonomy, and the corresponding GW polarizations are computed within the quadrupole approximation for extreme mass-ratio inspirals (EMRIs). We find that increasing ξ enhances the waveform amplitude and introduces a phase shift relative to the Schwarzschild case, with the peak characteristic strain increasing monotonically with ξ. The resulting signals peak in the millihertz band, falling within the sensitivity windows of future space-based detectors, indicating a qualitative path to future parameter constraints on quantum-gravity-induced deviations from classical general relativity in the strong-field regime.