Evolution of Killing fields in a pure matter space-time

Details Evolution of Killing fields in a pure matter space-time Evolution of Killing fields in a pure matter space-time

Jun 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978crasm.286.1163c&link_type=abstract

Academie des Sciences (Paris), Comptes Rendus, Serie A - Sciences Mathematiques, vol. 286, no. 23, June 12, 1978, p. 1163-1166.

Mathematics

1

Cosmic Dust, Field Theory (Physics), Relativity, Space-Time Functions, Einstein Equations, Hyperbolic Functions, Maxwell Equation, Vectors (Mathematics), Wave Propagation

Scientific paper

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., radiation-free) space-time. 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 space-time. This procedure ensures the existence of Killing fields in the vicinity of an initial hypersurface.

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