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

Abstract 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 $$Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> and the non-minimal coupling constant $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> increase, the radii of the marginally bound orbit ( $$r_{\text {MBO}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>MBO</mml:mtext> </mml:msub> </mml:math> ) and the innermost stable circular orbit ( $$r_{\text {ISCO}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>ISCO</mml:mtext> </mml:msub> </mml:math> ) decrease significantly, with corresponding reductions in the orbital energy $$E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> and angular momentum $$L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>L</mml:mi> </mml:math> . Furthermore, the allowable parameter space of energy and angular momentum ( $$E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> – $$L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>L</mml:mi> </mml:math> ) 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 $$Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> values towards the Schwarzschild case, as well as phase shifts, amplitude enhancement, and period shortening in the gravitational waveforms with increasing $$Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> and $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> . These results provide theoretical predictions for distinguishing different BH models through future gravitational wave observations.