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On the attractive force of the gravitational field in static space times†

Published online by Cambridge University Press:  24 October 2008

H. Müller zum Hagen
H. Müller zum Hagen
Affiliation:
King's College, London
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Abstract

A static metric is considered. A meaningful definition of gravitational force is given and the potential, which is the norm of the Killing vector ξa, is studied. For the case that the metric is asymptotically flat, the following is shown: The equi-potential surfaces are closed 2-dimensional surfaces S lying in the rest space V3, which is the hypersurface orthogonal to ξa. All the surfaces S enclose matter, and the gravitational force points into S towards the enclosed matter. A test particle starting at S will be pulled into the domain bounded by S and will never leave this domain.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 187 - 197
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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