Istvan Racz
On Einstein's Equations for Spacetimes Admitting a Non-Null Killing Field
Preprint series: ESI preprints

MSC:

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

Abstract: 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.

Keywords: Einstein equation, Killing field, matter fields