Initial Conditions in General Relativity: Lapse and Shift Formulation
- 1 August 1969
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 10 (8) , 1503-1507
- https://doi.org/10.1063/1.1664998
Abstract
We examine the system of coupled differential equations to which the constraints on the Cauchy data reduce if expressed in terms of the ``shift'' vector Nk and ``lapse'' N0. If (3)gij and ∂ (3)gij/∂t are given and Dirichlet boundary conditions are imposed, the solution Nk is found to be unique if 2 × (energy density) − (three‐curvature) > 0, but need not be unique when this inequality is not satisfied. No general existence theorem is known, but we list some conditions which make solutions impossible.Keywords
This publication has 1 reference indexed in Scilit:
- Three-Dimensional Geometry as Carrier of Information about TimePhysical Review B, 1962