Simonetta Frittelli
Einstein boundary conditions for the 3+1 Einstein equations
From the vanishing of the projection of the Einstein tensor along the
direction
normal to the boundary of the region of
integration, we derive necessary conditions on the boundary values of the
fundamental variables of the 3+1 Einstein equations,
consistent with constraint propagation [Frittelli and Gomez,
gr-qc/0302032].
Such conditions take the form of evolution
equations along the boundary and can be used to calculate the boundary
values
of certain components of the extrinsic curvature
and of the space derivatives of the metric. From a full analysis of the
spherically symmetric Einstein-Christoffel formulation
we show that, in the case of hyperbolic formulations, some of the conditions
provide welcome boundary values for some of the
incoming characteristic fields, whereas others constrain the values of some
of the outgoing characteristic fields.
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