Numerical investigations of the asymptotics of solutions to the evolutionary form of the constraints

Abstract

Systematic numerical investigations of the asymptotics of near Schwarzschild vacuum initial data sets is carried out by inspecting solutions to the parabolic-hyperbolic and to the algebraic-hyperbolic forms of the constraints, respectively. One of our most important findings is that the concept of near Schwarzschild configurations, applied previously in [4, 5], is far too restrictive. It is demonstrated that by relaxing the conditions on the freely specifiable part of the data a more appropriate notion of near Schwarzschild initial data configurations can be defined which allows us to generate asymptotically flat initial data configurations.

arXiv comment42 page, 12 figures

References in corpus (5)

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• Constraints as evolutionary systems
• Cauchy problem as a two-surface based `geometrodynamics'
• Asymptotics of solutions of a hyperbolic formulation of the constraint equations
• Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations

Cited by in corpus (6)

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• 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
• Hyperboloidal initial data without logarithmic singularities
• On the construction of Riemannian three-spaces with smooth inverse mean curvature foliation