Boundary Conditions for Constrained Systems of Evolution Equations in Numerical Relativity

Conference paper

Boundary Conditions for Constrained Systems of Evolution Equations in Numerical Relativity

Ledvinka, T.

In: Numerical Analysis and Applied Mathematics, American Institute of Physics, pp. 2029 (2011)

Abstract

In numerical relativity, to study astrophysical events such as black‐hole collisions, the Einstein equations for geometry of spacetime are solved as system of partial differential equations. Current simulations are usually based on so‐called BSSN system of 3+1 constrained hyperbolic evolution equations for tensorial fields of various ranks. The boundary conditions for evolved fields are given by the fact that the simulated events happen in an empty space and that far from the center the waves should propagate outwards. We analyze the usual outgoing radiation boundary conditions for the BSSN variables using potentials. Introduction of these potentials simplifies the linearized BSSN system into a set of wave equations. We also devise modifications of boundary conditions which prevent creation of constraint violations at boundary due to the conversion of outgoing constrained waves into ingoing unconstrained ones.

Institute authors

Ledvinka, Tomáš

Supported by

GACR 202/09/0772 — Current problems of gravitation, general relativity and relativistic astrophysics
MSM0021620860 — Fyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech

BibTeX

@inproceedings{UTF795,
  author        = {Ledvinka, T.},
  title         = {{Boundary Conditions for Constrained Systems of Evolution Equations in Numerical Relativity}},
  booktitle     = {Numerical Analysis and Applied Mathematics},
  publisher     = {American Institute of Physics},
  volume        = {1389},
  pages         = {2029},
  year          = {2011},
  doi           = {10.1063/1.3637014},
  url           = {https://aip.scitation.org/doi/10.1063/1.3637014},
}