Evolution of Killing fields in a pure matter spacetime
Abstract
A procedure which avoids the difficulties associated with Gaussian maps is applied to the study of the evolution of Killing fields in a pure matter (i.e., radiationfree) spacetime. The procedure relates the Killing field to an evolution system which is intrinsic and strictly hyperbolic, and the characteristic hypersurfaces associated with the system correspond to the propagation of the infinitesimal waves permitted by the problem physics (in this case, isotropic hypersurfaces and hypersurfaces generated by current lines). Necessary and sufficient conditions are presented for verifying Cauchy's data for the Einstein equations of this spacetime. This procedure ensures the existence of Killing fields in the vicinity of an initial hypersurface.
 Publication:

Academie des Sciences Paris Comptes Rendus Serie Sciences Mathematiques
 Pub Date:
 June 1978
 Bibcode:
 1978CRASM.286.1163C
 Keywords:

 Cosmic Dust;
 Field Theory (Physics);
 Relativity;
 SpaceTime Functions;
 Einstein Equations;
 Hyperbolic Functions;
 Maxwell Equation;
 Vectors (Mathematics);
 Wave Propagation;
 Astrophysics