Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ncimb..63..588t&link_type=abstract
Nuovo Cimento B, Serie 11, vol 63B, June 11, 1981, p. 588-600.
Astronomy and Astrophysics
Astronomy
1
Black Holes (Astronomy), Gravitational Fields, Quantum Mechanics, Relativity, Schwarzschild Metric, Two Body Problem, Electrons, Geodesy, Gravitation Theory
Scientific paper
Classical and quantum restrictions are derived for a test particle falling in the gravitational field of a Schwarzschild black hole. It is noted that in general relativity the gravitational mass of the particle increases (in contrast with Newtonian theory) and hence the condition that the test body exerts neglible influence on the central body becomes invalid for sufficiently small distance from the Schwarzschild radius. The effects of complementarity and the uncertainty principle are also discussed. This analysis also leads to an extremely small quantum distance below which the Schwarzschild geodesic motion is expected to break down. Both the classical and quantum restrictions are smaller than the Planck length for an in-falling electron.
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