Gravitational wave radiation from periodic orbits and quasi-periodic oscillations in an Einstein nonlinear Maxwell–Yukawa black hole

Abstract In this article, we investigate the orbital dynamics and quasi-periodic oscillations (QPOs) surrounding a static, spherically symmetric geometry of an Einstein–nonlinear Maxwell–-Yukawa (ENLMY) black hole (BH). Using the Hamiltonian formalism, we derive equations of motion and analyze the effective potential. We determine the innermost stable circular orbit (ISCO) and innermost bound circular orbit (IBCO) radii for different values of the Yukawa parameters $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> and $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> , and classify periodic orbits via rational frequency analysis, highlighting deviations from Schwarzschild geometry. We also study gravitational wave (GW) emission from periodic orbits and show how Yukawa terms affect GW signals. Fundamental frequencies are computed, and QPOs are analyzed using relativistic precession, warped disk, and tidal disruption models. By increasing $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> , the ENLMY spacetime effectively mimics the behavior of a Schwarzschild spacetime. Constraints on the BH mass and Yukawa parameters are derived using QPO data from stellar-mass (XTE J1550-564, GRO J1655-40, GRS 1915+105), intermediate-mass (M82 X-1), and supermassive (SgrA*) BHs within the relativistic precession model by employing a Markov chain Monte Carlo analysis.