Slow motion approximations in general relativity II. Gauge transformations

Details Slow motion approximations in general relativity II. Gauge transformations Slow motion approximations in general relativity II. Gauge transformations

Apr 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974gregr...5..119d&link_type=abstract

General Relativity and Gravitation, Volume 5, Issue 2, pp.119-137

Computer Science

Scientific paper

When the field equations of general relativity are expanded in powers of a small parameter, the general covariance of the exact theory implies a corresponding gauge invariance of the equations obtained in the expansion. In a slow motion expansion, the derivation of this gauge transformation is complicated by the fact that the time coordinate is singled out for special treatment. In a previous paper, a new (3 + 1)-dimensional decomposition of the field equations was obtained which is particularly suitable as a starting point for slow motion approximations. The present paper gives a systematic method, again using covariant techniques throughout, for obtaining the corresponding gauge transformations to arbitrarily high accuracy. The calculations are explicitly carried out as far as is required in the 2 1/2-post-Newtonian approximation.

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