Gravitational wave signatures of periodic orbits around a Schwarzschild-like black hole

Abstract

We investigate how deviations from the Schwarzschild geometry affect the motion of massive test particles and the gravitational radiation associated with their periodic trajectories around a new improved Schwarzschild black hole. Periodic configurations are determined by examining the commensurability of the radial and azimuthal orbital frequencies. For representative trajectories, we numerically reconstruct the particle motion and calculate corresponding gravitational wave polarizations using the symmetric trace-free mass-quadrupole approach. By comparing these signals with their Schwarzschild counterparts, we assess how the modified spacetime geometry is encoded in the radiation. Our analysis shows that the parameters $\xi$ and $\gamma$ produce modest changes in the orbital configurations and their associated waveforms, providing a means of investigating the dynamical signatures of this BH model.