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

Details On Einstein's equations for spacetimes admitting a non-null Killing field On Einstein's equations for spacetimes admitting a non-null Killing field

1993-11-04

arxiv.org/abs/gr-qc/9311006v2

J.Math.Phys. 38 (1997) 4237-4254

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, TeX

Scientific paper

10.1063/1.532092

We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. 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 resolvent systems of partial differential equations for the basic field variables. Finally, the above results are applied for perfect fluid spacetimes describing possible equilibrium configurations of relativistic dissipative fluids.

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