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In this work, we study gravitational wave emission from periodic orbits of test particles, analyze quasi periodic oscillations, and constrain the parameters of the static, spherically symmetric Einstein nonlinear Maxwell Yukawa black hole. 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 and innermost bound circular orbit, illustrating how the Yukawa screening parameter 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 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.
Shabbir et al. (Sat,) studied this question.