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Studying particle motion in the gravitational field of a black hole from theperspective of different observers is important for separating the coordinateartifacts from the physical phenomena. In this paper, we show that a freelyfalling test particle exhibits gravitational repulsion by a black hole as seenby an asymptotic observer, whereas nothing of the kind happens as recorded by afreely falling observer or by an observer located at a finite distance from theevent horizon. This analysis is carried out for a general Reissner-Nordstr\"om,an extremal Reissner-Nordstr\"om, and a Schwarzschild black hole. We are leadto conclude that the origin of these bizarre results lies in the fact that thequantities measured by the different observers are neither Lorentz scalars norgauge invariant.

Hilbert repulsion in the Reissner-Nordstr\"om and Schwarzschild spacetimes