Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-02-24
Phys.Rev.D81:084014,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Replaced by the published version. Some clarifications and references added.
Scientific paper
10.1103/PhysRevD.81.084014
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)].
Brizuela David
Schaefer Gerhard
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