Gravitational wave signatures of magnetized Ernst black hole

We investigate gravitational wave (GW) emission from periodic timelike orbits of a test particle around a magnetized Ernst black hole and the gravitational waveforms generated by their orbital dynamics. The bound geodesics are systematically classified using the zoom-whirl representation labeled with three integers $(z,w,v)$. Gravitational waveforms are computed within a numerical framework that combines exact geodesic motion with the quadrupole approximation, which is well-suited to extreme mass-ratio inspirals (EMRIs). This analysis is particularly relevant for assessing the capability of future gravitational-wave observations to detect the effects of magnetic fields. Our results show that an intrinsic magnetic field imprints characteristic features on the GW signal, highlighting GW astronomy as a promising avenue for probing magnetized black hole spacetimes.