On homogeneous solutions of Einstein's field equations

Details On homogeneous solutions of Einstein's field equations On homogeneous solutions of Einstein's field equations

Apr 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978gregr...9..299h&link_type=abstract

General Relativity and Gravitation, vol. 9, Apr. 1978, p. 299-327.

Mathematics

Einstein Equations, Field Theory (Physics), Space-Time Functions, Tensors, Energy Methods, Lie Groups, Minkowski Space, Transformations (Mathematics)

Scientific paper

A method is explained for determining all homogeneous solutions to the Einstein field equations for all possible energy-momentum tensors. The rudiments of the formalism for homogeneous spaces are developed, the Lie algebras over the reals are classified into nine different broad groups using the Lorentz group only, and the components of the Ricci tensor field are computed separately for the nine major types. The vacuum field equations are then imposed, and all the homogeneous solutions to these equations are constructed. The solutions are found to include two families of Robinson waves as well as the homogeneous type I Petrov solution.

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