Uniqueness of the equilibrium configurations of slowy rotating relativistic fluids
We consider the equations of a general relativistic space-time that is stationary, asymptotically Euclidean, diffeomorphic to R/sup 4/ and consists of an exterior vacuum solution and an interior perfect fluid in rigid motion. If one requires further that the solution be close to the static spherically symmetric ones (in the sense of a suitable topology on the set of stationary space--time metrics) it is shown that for a given equation of state rho( p) and given total mass m and (small) angular momentum J there are no smooth curves of physically distinct global axially symmetric solutions. In view of a recent result of Lindblom that all such space-times are axisymmetric this result is quite general. The method is a generalization of the one used to prove (in a ''local'' sense) the uniqueness of the spherical solution in the static case.
- Research Organization:
- Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- OSTI ID:
- 6895267
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Vol. 21:11
- Country of Publication:
- United States
- Language:
- English
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