Construction of high precision numerical single and binary black hole initial data

Abstract

We present a novel implicit numerical implementation of the parabolic-hyperbolic formulation of the constraints of general relativity. The proposed method is unconditionally stable, has the advantage of not requiring the imposition of any boundary conditions in the strong field regime, and offers a holistic (all inclusive) approach to the construction of single and binary black hole initial data. The new implicit solver is extensively tested against known exact black hole solutions and is used to construct initial data for several single and binary black hole configurations.

17 pages, 10 figures

References in corpus (2)

• Cauchy problem as a two-surface based `geometrodynamics'
• Black hole initial data by numerical integration of the parabolic-hyperbolic form of the constraints

Cited by in corpus (4)

• Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations
• Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
• Is it possible to construct asymptotically flat initial data using the evolutionary forms of the constraints?
• Black hole initial data by numerical integration of the parabolic-hyperbolic form of the constraints