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Constraint-preserving boundary conditions in numerical relativity

Constraint-preserving boundary conditions in numerical relativity
Constraint-preserving boundary conditions in numerical relativity
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints’ propagation in 3D unconstrained numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally coupled scalar field, within the Einstein-Christoffel (EC) symmetric hyperbolic formulation of Einstein’s equations. By exploiting the characteristic propagation of the main variables and constraints, we are able to single out the only free modes at the outer boundary for these problems. In the vacuum case a single free mode exists which corresponds to a gauge freedom, while in the matter case an extra mode exists which is associated with the scalar field. We make use of the fact that the EC formulation has no superluminal characteristic speeds to excise the singularity. We present a second-order, finite difference discretization to treat these scenarios, where we implement these constraint-preserving boundary conditions, and are able to evolve the system for essentially unlimited times (i.e., limited only by the available computing time). As a test of the robustness of our approach, we allow large pulses of gauge and scalar field to enter the domain through the outer boundary. We reproduce expected results, such as trivial (in the physical sense) evolution in the vacuum case (even in gauge-dynamical simulations), and the tail decay for the scalar field.
1550-7998
1-13
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Lehner, Luis
1b8c9b8f-a6d4-4448-ab80-1dca2b6ad312
Tiglio, Manuel
70c1e9ee-b30c-4354-af43-1bd3b4b6af24
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Lehner, Luis
1b8c9b8f-a6d4-4448-ab80-1dca2b6ad312
Tiglio, Manuel
70c1e9ee-b30c-4354-af43-1bd3b4b6af24

Calabrese, Gioel, Lehner, Luis and Tiglio, Manuel (2002) Constraint-preserving boundary conditions in numerical relativity. Physical Review D, 65 (10), 1-13. (doi:10.1103/PhysRevD.65.104031).

Record type: Article

Abstract

This is the first paper in a series aimed to implement boundary conditions consistent with the constraints’ propagation in 3D unconstrained numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally coupled scalar field, within the Einstein-Christoffel (EC) symmetric hyperbolic formulation of Einstein’s equations. By exploiting the characteristic propagation of the main variables and constraints, we are able to single out the only free modes at the outer boundary for these problems. In the vacuum case a single free mode exists which corresponds to a gauge freedom, while in the matter case an extra mode exists which is associated with the scalar field. We make use of the fact that the EC formulation has no superluminal characteristic speeds to excise the singularity. We present a second-order, finite difference discretization to treat these scenarios, where we implement these constraint-preserving boundary conditions, and are able to evolve the system for essentially unlimited times (i.e., limited only by the available computing time). As a test of the robustness of our approach, we allow large pulses of gauge and scalar field to enter the domain through the outer boundary. We reproduce expected results, such as trivial (in the physical sense) evolution in the vacuum case (even in gauge-dynamical simulations), and the tail decay for the scalar field.

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Published date: 2002

Identifiers

Local EPrints ID: 40862
URI: http://eprints.soton.ac.uk/id/eprint/40862
ISSN: 1550-7998
PURE UUID: 3977149a-90d9-4e81-94a3-54bdb09c0ded

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Date deposited: 11 Jul 2006
Last modified: 16 Mar 2021 17:43

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