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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Communicated by Vincent Rivasseau.
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Choquet-Bruhat, Y., Chruściel, P.T. & Martín-García, J.M. The Cauchy Problem on a Characteristic Cone for the Einstein Equations in Arbitrary Dimensions. Ann. Henri Poincaré 12, 419–482 (2011). https://doi.org/10.1007/s00023-011-0076-5
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DOI: https://doi.org/10.1007/s00023-011-0076-5