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arXiv · 1002.4552

Fourth-post-Newtonian-exact approximation to General Relativity

David Brizuela·Gerhard Schaefer
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Abstract

An approximation to General Relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved equations are explicitly elliptic except the wave equation that describes the two independent degrees of freedom of the gravitational field. The formalism covers naturally the conformal-flat-condition (CFC) approach by Isenberg, Wilson, and Mathews and the improved second PN-order exact approach CFC+. For stationary configurations, like Kerr black holes, agreement with General Relativity is achieved even through 5PN order. In addition, a particularly interesting 2PN-exact waveless approximation is analyzed in detail, which results from imposing more restrictive conditions. The proposed scheme can be considered as a further development on the waveless approach suggested by Schaefer and Gopakumar [Phys. Rev. D {\bf 69}, 021501 (2004)].

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David Brizuela, Gerhard Schaefer. 2010-04-12. Fourth-post-Newtonian-exact approximation to General Relativity. https://doi.org/10.1103/physrevd.81.084014

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