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The problem of exact interior solutions for rotating rigid bodies in general relativityThe (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.
Document ID
19930054459
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Wahlquist, H. D.
(JPL Pasadena, CA, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1993
Publication Information
Publication: Journal of Mathematical Physics
Volume: 33
Issue: 1
ISSN: 0022-2488
Subject Category
Physics (General)
Accession Number
93A38456
Distribution Limits
Public
Copyright
Other

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