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New Homogeneous Solutions of Einstein's Field Equations with Incoherent Matter Obtained by a Spinor Technique

### Abstract

Einstein's field equations with incoherent matter are solved for the case of homogeneous spacetime, i.e., for metrics allowing a four parametric simply transitive group of motions. Two families of new solutions are obtained by use of a spinor technique. As a special result a proof emerges for Gödel's theorem, which states that there exist only two homogeneous solutions of Einstein's field equations with incoherent matter and rigid rotation, namely the Gödel cosmos and the Einstein static universe.

© 1965 The American Institute of Physics

Received 14 April 1964
Published online 22 December 2004

/content/aip/journal/jmp/6/4/10.1063/1.1704311

http://aip.metastore.ingenta.com/content/aip/journal/jmp/6/4/10.1063/1.1704311

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