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arXiv · 1006.4467

The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions

Yvonne Choquet-Bruhat·Piotr T. Chruściel·José M. Martín-García
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Abstract

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. 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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Yvonne Choquet-Bruhat, Piotr T. Chruściel, José M. Martín-García. 2010-06-23. The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions. https://doi.org/10.1007/s00023-011-0076-5

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