Worldtube conservation laws for the null-timelike evolution problem

Abstract

I treat the worldtube constraints which arise in the null-timelike initial-boundary value problem for the Bondi-Sachs formulation of Einstein's equations. Boundary data on a worldtube and initial data on an outgoing null hypersurface determine the exterior spacetime by integration along the outgoing null geodsics. The worldtube constraints are a set of conservation laws which impose conditions on the integration constants. I show how these constraints lead to a well-posed initial value problem governing the extrinsic curvature of the worldtube, whose components are related to the integration constants. Possible applications to gravitational waveform extraction and to the well-posedness of the null-timelike initial-boundary value problem are discussed.

Article submitted to Gen. Rel. Grav. issue dedicated to Josh Goldburg

References in corpus (1)

• Problems which are well-posed in a generalized sense with applications to the Einstein equations

Cited by in corpus (6)

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• Affine-null metric formulation of General Relativity at two intersecting null hypersurfaces
• Fully relativistic three-dimensional Cauchy-characteristic matching for physical degrees of freedom
• The affine-null metric formulation of Einstein's equations
• Boundary Conditions for the Gravitational Field
• Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry