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.