Periodic Orbits and Gravitational Wave Signatures around the Bonanno--Reuter Regular Black Hole

Abstract

Timelike geodesics, periodic orbits, and their associated gravitational-wave signatures are examined in the spacetime of a Bonanno--Reuter regular black hole, a geometry arising from Asymptotically Safe Gravity in which a running Newton coupling replaces the central singularity with a de Sitter core. The dimensionless parameter $α/M^2$ completely determines the strong-field dynamics. Increasing $α/M^2$ shifts the marginally bound and innermost stable circular orbits inward, systematically reducing their characteristic radii, angular momenta, and energies; the allowed phase space for bound motion contracts accordingly. Classifying trajectories via the rational frequency ratio $q = w + v/z$ reveals that periodic orbits experience a mild inward contraction, which reduces the energy necessary to sustain a specific topology. Within the numerical kludge framework, we calculate the gravitational-wave polarizations for extreme mass-ratio inspirals. The asymptotically safe correction induces a leftward phase shift that reflects shorter orbital periods, while mildly enhancing peak amplitudes owing to the smaller periastron distances reached in the deep strong-field regime. Waveform sensitivity displays a strong dependence on topology, with high-whirl orbits, which persist longer in the strong-field region near the horizon, showing markedly more pronounced deviations. Unlike environmental effects that inflate orbital scales, intrinsic quantum-gravity modifications generate distinct, observationally detectable signatures for future space-based detectors such as LISA, Taiji, and TianQin.