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Hilbert repulsion in the Reissner-Nordstr\"om and Schwarzschild spacetimes
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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.
Forward citations
Cited by 2 Pith papers
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Nonstatic Reissner-Nordstr\"om metric in the perturbative $f(R)$ theory: Embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation
The paper claims that charged spherically symmetric sources in perturbative f(R) gravity can radiate gravitational waves through a time-dependent exterior metric.
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On the effect of gravitational repulsion on geodesic deviation in the Schwarzschild-de Sitter spacetime
Geodesic-deviation coefficients C00 and C10 vanish and extremize at the SdS critical surface r=(3M/Λ)^{1/3}, marking the switch between gravitational attraction and repulsion for radial tardyons.
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