Probing the nature of Einstein-nonlinear Maxwell-Yukawa black hole through gravitational wave forms from periodic orbits and quasiperiodic oscillations

In this work, we study gravitational-wave (GW) emission from periodic orbits of test particles, analyze quasi-periodic oscillations (QPOs), and constrain the parameters of the static, spherically symmetric Einstein–nonlinear Maxwell–Yukawa (ENLMY) black hole (BH). Using the Hamiltonian approach, we calculate the equations of motion of the particles. We analyze the effective potential to determine the innermost stable circular orbit (ISCO) and innermost bound circular orbit (IBCO), illustrating how the Yukawa screening parameter α and electric charge Q affect orbital stability and energy requirements. Periodic orbits are classified by integer triplets and exhibit characteristic zoom-whirl behavior. Based on these orbits, we compute the corresponding GW signals in both the h + and h × polarizations. Finally, we perform Monte Carlo Markov Chain (MCMC) simulations to constrain the parameters of the ENLMY BH for four microquasars and the galactic center within the relativistic precession model.