Non-minimally coupled Einstein–Yang–Mills black holes: periodic orbits and gravitational wave radiation in extreme mass ratio systems

As one of the key targets for future space-based gravitational wave detectors, extreme-mass-ratio inspirals (EMRIs) offer valuable observational clues for testing strong-field gravity and classifying black holes through their orbital dynamics and gravitational wave emission characteristics. This work systematically investigates the transitional periodic orbits of test particles and their single-cycle gravitational radiation features in the background of non-minimally coupled Einstein–Yang–Mills (EYM) BHs. The results show that as the magnetic charge parameter Q Q and the non-minimal coupling constant ξ ξ increase, the radii of the marginally bound orbit ( rMBO r MBO ) and the innermost stable circular orbit ( rISCO r ISCO ) decrease significantly, with corresponding reductions in the orbital energy E E and angular momentum L L . Furthermore, the allowable parameter space of energy and angular momentum ( E E – L L ) for bound orbits shifts towards the left. We then plot typical periodic orbits through orbit classification, finding that the non-minimal coupling effect suppresses the orbital contraction induced by the magnetic charge, leading to degeneracy of orbits with different Q Q values towards the Schwarzschild case, as well as phase shifts, amplitude enhancement, and period shortening in the gravitational waveforms with increasing Q Q and ξ ξ . These results provide theoretical predictions for distinguishing different BH models through future gravitational wave observations.