Worldtube conservation laws for the null-timelike evolution problem |
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Authors: | Jeffrey Winicour |
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Institution: | 1.Department of Physics and Astronomy,University of Pittsburgh,Pittsburgh,USA;2.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Golm,Germany |
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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. |
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