Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-07-02
Astron.Nachr. 324 (2003) 485-488
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages; text accepted for publication by Astronomische Nachrichten
Scientific paper
10.1002/asna.200310093
The so called gamma metric corresponds to a two-parameter family of axially symmetric, static solutions of Einstein's equations found by Bach. It contains the Schwarzschild solution for a particular value of one of the parameters, that rules a deviation from spherical symmetry. It is shown that there is invariantly definable singular behaviour beyond the one displayed by the Kretschmann scalar when a unique, hypersurface orthogonal, timelike Killing vector exists. In this case, a particle can be defined to be at rest when its world-line is a corresponding Killing orbit. The norm of the acceleration on such an orbit proves to be singular not only for metrics that deviate from Schwarzschild's metric, but also on approaching the horizon of Schwarzschild metric itself, in contrast to the discontinuous behaviour of the curvature scalar.
Antoci Salvatore
Liebscher Dierck Ekkehard
Mihich L.
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