Abubakir Shermatov

We study circular geodesics and quasi–periodic oscillations (QPOs) around a static black hole (BH) in f ( R , T ) gravity surrounded by a Kiselev radiation field with equation of state parameter w = 1 / 3 . Starting from the exact analytic solution, we introduce an effective mass function and show how the radiation parameter K and the f ( R , T ) coupling γ deform the BH geometry, reducing the effective gravitational mass near the BH while recovering the standard behavior at large radii. For electrically neutral test particles, we derive the effective potential, the specific energy and angular momentum of circular orbits, and the characteristics of the innermost stable circular orbit (ISCO), the marginally bound orbit, and the marginally circular orbit, highlighting their dependence on the radiation field. We then compute the Keplerian (orbital) and radial/vertical epicyclic frequencies along ISCOs and analyze how the radiation field and f ( R , T ) couplings modify these dynamical frequencies. Finally, we confront the model with twin–peak QPO observations from the microquasars XTE J1550–564 and GRO J1655–40, the intermediate–mass BH M82 X-1, and Sgr A* by applying the relativistic precession (RP) and warped–disk (WD) QPO models. Using χ 2 minimization, we perform Monte Carlo Markov Chain simulations to constrain the parameters ( M , α , K , γ , r QPO ) . Our fits show that the RP model provides consistent descriptions for GRO J1655–40, M82 X-1, and Sgr A*, while the WD model is mainly favored for XTE J1550–564, and that the inferred values of K and γ are largely degenerate between the two QPO scenarios.

We study the motion of neutral test particles around a phantom Reissner--Nordström Anti-de Sitter (RN--AdS) black hole (BH) with non-commutative (NC) corrections. We analyze circular motion through the effective potential and calculate the Keplerian, radial epicyclic, and vertical epicyclic frequencies. We show that the phantom field and NC parameter modify the stable circular orbits and shift the ISCO radius. We then apply these results to the RP and WD models of twin-peak quasi-periodic oscillations and find noticeable deviations from the Schwarzschild case in the corresponding frequency relations.

We investigate a static Kiselev black hole solution in f(R,T) gravity. We then study equatorial motion of test particles by incorporating the matter–geometry coupling through the non-geodesic equation, which modifies the effective potential via a weak-coupling parameter α. The Keplerian and epicyclic frequencies are derived and employed to model twin-peak QPOs. Finally, using χ^2 minimization and Bayesian MCMC sampling with Gaussian priors, we constrain the model parameters with QPO data for intermediate mass black hole M82 X–1.

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.