The problem of exact interior solutions for rotating rigid bodies in general relativity.

Details The problem of exact interior solutions for rotating rigid bodies in general relativity. The problem of exact interior solutions for rotating rigid bodies in general relativity.

Jan 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992jmp....33..304w&link_type=abstract

Journal of Mathematical Physics, Vol. 33, No. 1, p. 304 - 335

Mathematics

Mathematical Physics

12

Scientific paper

The (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 Ω, 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. 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.

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