Hilbert repulsion in the Kerr–Newman anti-de Sitter spacetime

In this work, we investigate the existence of Hilbert or gravitational repulsion of a test charged particle near the Kerr–Newman anti-de Sitter black hole. We found that the dynamical motion of the test charged particle is significantly affected by the black hole charge and spin, probably due to the electrostatic interaction and the curvature behaviour of spacetime. We also obtain the various conditions under which a freely falling test particle towards the black hole experiences the Hilbert repulsion or attraction as viewed by a distant observer.