Curled orbit and epicyclic oscillation of charged particles around the weakly magnetized black hole in the presence of Lorentz violation

In this paper, we investigate the motion of charged particles around the weakly magnetized Schwarzschild-like bumblebee black hole which has Lorentz symmetry breaking. Charged particles have curled orbits around the black hole which can only appear in the presence of external magnetic field. We investigate the effect of Lorentz violation factor on the curled orbit for both the case with and without cosmological constant. Furthermore, we investigate the harmonic oscillation behavior of the charged particles around the stable circular orbit. By using the epicyclic resonance model, we relate the harmonic oscillations of charged particles to the twin high frequency quasi-periodic oscillations observed in micro-quasars. Based on the observations of quasi-periodic oscillation, we provide a stringent constraint on the Lorentz violating parameters by using Markov Chain Monte Carlo algorithm. As the black hole shadow for Schwarzschild-like bumblebee black hole degenerates to the ordinary Schwarzschild black hole, the constraints we obtained from the quasi-period oscillation is crucial for further searching for the imprint of Lorentz symmetry breaking in our universe.