Worldtube conservation laws for the null-timelike evolution problem

Understand

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.