Slow motion approximations in general relativity II. Gauge transformations

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.