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

TL;DR

This paper investigates how different observers perceive gravitational effects near black holes, revealing that a freely falling particle appears repelled by the black hole to distant observers, but not to local ones, due to observer-dependent measurements.

Contribution

It demonstrates that gravitational repulsion effects depend on the observer's frame, highlighting the importance of gauge-invariant quantities in black hole physics.

Findings

Distant observers see gravitational repulsion of free particles near black holes.

Local observers do not observe such repulsion, indicating observer-dependent phenomena.

The results are consistent across Reissner-Nordström and Schwarzschild black holes.

Abstract

Studying particle motion in the gravitational field of a black hole from the perspective of different observers is important for separating the coordinate artifacts from the physical phenomena. In this paper, we show that a freely falling test particle exhibits gravitational repulsion by a black hole as seen by an asymptotic observer, whereas nothing of the kind happens as recorded by a freely falling observer or by an observer located at a finite distance from the event horizon. This analysis is carried out for a general Reissner-Nordstr\"om, an extremal Reissner-Nordstr\"om, and a Schwarzschild black hole. We are lead to conclude that the origin of these bizarre results lies in the fact that the quantities measured by the different observers are neither Lorentz scalars nor gauge invariant.