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Solutions of Einstein's Equations for a Fluid Which Exhibit Local Rotational Symmetry

### Abstract

All solutions of Einstein's equations for pressure‐free matter which exhibit local rotational symmetry were classified in an earlier paper by one of us. This paper extends the earlier theory to the case of a general fluid, with an electromagnetic field possibly present. A classification of these solutions for a perfect fluid is given, and assuming a physically reasonable equation of state, some exact solutions of cosmological interest are obtained. Finally, the difficulties encountered when extending the treatment to a general fluid are discussed; the same general classification can be made.

© 1968 The American Institute of Physics

Received 14 August 1967
Published online 28 October 2003