Worldtube conservation laws for the null-timelike evolution problem

Details Worldtube conservation laws for the null-timelike evolution problem Worldtube conservation laws for the null-timelike evolution problem

2011-05-17

arxiv.org/abs/1105.3493v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

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.

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