Taxonomy of periodic orbits and gravitational waves in a deformed Schwarzschild black hole spacetime

Abstract: In this paper, we investigate periodic orbits of test particles around a deformed Schwarzschild black hole and the resulting gravitational waves. Firstly, we examine the properties of circular orbits and find that circular orbits could disappear when the deformation is large enough. Then, using an orbital taxonomy, we characterize various periodic orbits with a set of triples, which describes the zoom-whirl behaviours. We also calculate the gravitational waveform signals generated by different periodic orbits, revealing the influence of the deformation on the gravitational wave, which can be potentially picked up by future space-based detectors.