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

Abstract

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.

41 pages, no figures, accepted for publication in Phys. Rev. D, significant revision in presentation (including added references and corrected typos)

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Cited by in corpus (15)

• Binary-black-hole initial data with nearly-extremal spins
• Nonrotating black hole in a post-Newtonian tidal environment
• Geometry and dynamics of a tidally deformed black hole
• The Current Status of Binary Black Hole Simulations in Numerical Relativity
• Conformally curved binary black hole initial data including tidal deformations and outgoing radiation
• Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors
• Conformal Thin-Sandwich Solver for Generic Initial Data
• Gravitational waves from merging compact binaries
• Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions
• Construction of initial data for 3+1 numerical relativity
• Approximate initial data for binary black holes
• Including realistic tidal deformations in binary black-hole initial data
• Binary black hole evolutions of approximate puncture initial data