General Relativity and Gravitation

, Volume 43, Issue 12, pp 3269–3288 | Cite as

Worldtube conservation laws for the null-timelike evolution problem

  • Jeffrey WinicourEmail author
Research Article


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.


Conservation laws Gravitational waves Boundary conditions 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of PittsburghPittsburghUSA
  2. 2.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutGolmGermany

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