Post-Newtonian Freely Specifiable Initial Data for Binary Black Holes in Numerical Relativity

Details Post-Newtonian Freely Specifiable Initial Data for Binary Black Holes in Numerical Relativity Post-Newtonian Freely Specifiable Initial Data for Binary Black Holes in Numerical Relativity

2005-09-30

arxiv.org/abs/gr-qc/0509128v2

Phys.Rev. D73 (2006) 124002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

41 pages, no figures, accepted for publication in Phys. Rev. D, significant revision in presentation (including added referenc

Scientific paper

10.1103/PhysRevD.73.124002

Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically realistic freely specifiable initial data for binary black hole systems in numerical relativity, which are in agreement with post-Newtonian results. Following the approach taken by Blanchet, we propose a particular solution to the time-asymmetric constraint equations, which represent a system of two moving black holes, in the form of the standard conformal decomposition of the spatial metric and the extrinsic curvature. The solution for the spatial metric is given in symmetric tracefree form, as well as in Dirac coordinates. We show that the solution differs from the usual post-Newtonian metric up to the 2PN order by a coordinate transformation. In addition, the solutions, defined at every point of space, differ at second post-Newtonian order from the exact, conformally flat, Bowen-York solution of the constraints.

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