Constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation in spherical symmetry

Abstract

We introduce a set of constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations in spherical symmetry, based on its hyperbolic structure. While the outgoing eigenfields are left to propagate freely off the numerical grid, boundary conditions are set to enforce that the incoming eigenfields don't introduce spurious reflections and, more importantly, that there are no fields introduced at the boundary that violate the constraint equations. In order to do this we adopt two different approaches to set boundary conditions for the extrinsic curvature, by expressing either the radial or the time derivative of its associated outgoing eigenfield in terms of the constraints. We find that these boundary conditions are very robust in practice, allowing us to perform long lasting evolutions that remain accurate and stable, and that converge to a solution that satisfies the constraints all the way to the boundary.

15 pages, 12 figures, to be published in Classical and Quantum Gravity

References in corpus (7)

• Covariant formulations of BSSN and the standard gauge
• Improved outer boundary conditions for Einstein's field equations
• Towards absorbing outer boundaries in General Relativity
• Initial boundary value problems for Einstein's field equations and geometric uniqueness
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Cited by in corpus (2)

• Critical gravitational collapse of a massive complex scalar field
• Critical gravitational collapse of a non-minimally coupled scalar field