Asymptotics of solutions of a hyperbolic formulation of the constraint equations
arXiv:1706.06700 · doi:10.1088/1361-6382/aa8be6
Abstract
In this paper we consider the hyperbolic formulation of the constraints introduced by Rácz. Using the numerical framework recently developed by us we construct initial data sets which can be interpreted as nonlinear perturbations of Schwarzschild data in Kerr-Schild coordinates and investigate their asymptotics. Our results suggest that, unless one finds a way to exploit the freedom to pick the free part of the initial data in some suitable way, generic initial data sets obtained by this method may violate fundamental asymptotic conditions.
arXiv comment26 pages, 10 figures
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- Toward computing gravitational initial data without elliptic solvers
- Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
- Explorations of the infinite regions of space-time
- Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints
- Is it possible to construct asymptotically flat initial data using the evolutionary forms of the constraints?