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IX.—The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry

Published online by Cambridge University Press:  15 September 2014

W. J. van Stockum
W. J. van Stockum
Affiliation:
Mathematical Institute, University of Edinburgh
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Extract

The generalisation to the stationary case of the solution given by Weyl (1918) of Einstein's gravitational equations in a statical axially symmetric universe, has been attempted by various writers. It has not, however, so far been possible to reduce the equations to linear form and thus to find the most general solution. A set of special solutions has been obtained by Lewis (1932), valid in a region free of matter, which contain Weyl's solution as a particular case. They depend upon an arbitrary solution of the equation

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 57 , 1938 , pp. 135 - 154
Copyright
Copyright © Royal Society of Edinburgh 1938

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References

References to Literature

Lewis, T., 1932. “Some Special Solutions of the Equations of Axially Symmetric Fields,” Proc. Roy. Soc., A, vol. cxxxvi, pp. 176–192.Google Scholar
Walker, A. G., 1935. “Note on Relativistic Mechanics,” Proc. Edin. Math. Soc., vol. iv, pp. 170–174.CrossRefGoogle Scholar
Weyl, H., 1918. “Zur Gravitationstheorie,” Ann. Phys. Lpz., pp. 117–145.Google Scholar