Elsevier

Physics Letters A

Volume 120, Issue 3, 9 February 1987, Pages 119-123
Physics Letters A

Non-existence of stationary, axisymmetric dust solutions of Einstein's equations on spatially compact manifolds

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Abstract

By using a theorem on the classifacation of SO(2)-actions on three-dimensional manifolds, it is shown that axisymmetric, stationary solutions of Einstein's equations do not exist on spacetimes with compact, space-like hypersurfaces, provided that the energy-momentum tensor is trace-free in the two-dimensional space of trajectories.

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