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Charged particle and epicyclic motions around $4D$ Einstein-Gauss-Bonnet black hole immersed in an external magnetic field

We investigate particle motion in the vicinity of a $4D$ Einstein-Gauss-Bonnet (EGB) black hole immersed in external asymptotically uniform magnetic field. It is well known that magnetic fields can strongly affect charged particle motion in the black hole vicinity due to the Lorenz force. We find that the presence of the Gauss-Bonnet (GB) coupling gives rise to a similar effect, reducing the radius of the innermost stable circular orbit (ISCO) with respect to the purely relativistic Schwarzschild black hole. Further, we consider particle collisions in the black hole vicinity to determine the center of mass energy and show that this energy increases with respect to the Schwarzschild case due to the effect of the GB term. Finally, we consider epicyclic motion and its frequencies and resonance as a mean to test the predictions of the model against astrophysical observations. In particular we test which values of the parameters of the theory best fit the 3:2 resonance of high-frequency quasi-periodic oscillations in three low-mass X-ray binaries.