Higher Order Gravitational Potential for Many-Body System

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Abstract
Gravitational potential for many-body system is obtained up to post-post-Newtonian order of approximation from the metric tensor derived previously, which is Minkowskian at spatial infinity. The calculation is based on the Lagrangian of Fokker type. The transverse-traceless part of the metric tensor contributes to the potential of post-post-Newtonian order, even to the G3-static part. The fact that the G3-static potential includes the contribution from the transverse-traceless part is the manifestation of non-linear nature of the theory of gravity. The gravitational potential obtained here coincides with that calculated in the canonical formalism, but does not coincide with that obtained in the conventional formalism of quantized theory.

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