Slow-motion approximations in general relativity I. Decomposition of the field equations

Details Slow-motion approximations in general relativity I. Decomposition of the field equations Slow-motion approximations in general relativity I. Decomposition of the field equations

Oct 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972gregr...3..227d&link_type=abstract

General Relativity and Gravitation, Volume 3, Issue 3, pp.227-249

Computer Science

2

Scientific paper

A new (3+1)-dimensional decomposition of the Einstein gravitational field equations is obtained for a general spacetime. The metric is taken in the form ds^2 = e^{ - 2u} k_{ab} (dx^a + ξ ^a dt)(dx^b + ξ ^b dt) - c^2 e^{2u} dt^2 and the resulting equations treatk ab as the metric in the space-like hypersurfacest=constant. It is shown that this decompostion forms a more convenient starting point for slow motion approximations than does their usual 4-dimensional formulation. This is illustrated by a derivation of the first post-Newtonian approximation to the field equations, the simplicity there resulting fromk ab being still flat to this order.

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