The Cauchy Problem on a Characteristic Cone for the Einstein Equations in Arbitrary Dimensions |
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Authors: | Yvonne Choquet-Bruhat Piotr T Chru?ciel Jos?? M Mart??n-Garc??a |
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Institution: | (1) Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA |
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Abstract: | We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary space–time
dimensions n + 1 ≥ 3. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution
of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge
also satisfies the full Einstein equations. We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum
case. |
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