On Einstein's equations for spacetimes admitting non-null Killing fields

Rácz, István (1997) On Einstein's equations for spacetimes admitting non-null Killing fields. JOURNAL OF MATHEMATICAL PHYSICS, 38. pp. 4237-4254. ISSN 0022-2488

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Abstract

We consider the three-dimensional formulation of Einstein's theory for space-times possessing a non-null Killing field ξ^a. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be shown here how this result can be generalized for the case of essentially arbitrary matter fields. The systematic study of the structure of the fundamental field equations is carried out. In particular, the existence of geometrically preferred reference systems is shown. Using local coordinates of this type two approaches are presented resulting in resolvent systems of partial differential equations for the basic field variables. Finally, the above results are applied for perfect fluid space-times describing possible equilibrium configurations of relativistic dissipative fluids. © 1997 American Institute of Physics.

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