A numerical solver for Einstein's constraint equations as a parabolic-hyperbolic system

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Written by Christian Schell

Einstein's field equations contain a system of constraints.
Very often they are considered as elliptic equations (with benefits but also drawbacks).
Only recently István Rácz initiated systematic studies of the constraints as an evolutionary system.
In this talk I will review some of the basics and present a numerical verification of the previously obtained analytical results.
I consider linear perturbations of Minkowski spacetime and the full nonlinear equations in axisymmetry.
This is part of a joint project with Oliver Rinne to model Einstein's axisymmetric vacuum equations in a constrained evolution scheme using spherical polar coordinates with a regular center.