caa a22 4500 445320311 CHVBK 20180317142701.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00023-011-0076-5 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0076-5 The Cauchy Problem on a Characteristic Cone for the Einstein Equations in Arbitrary Dimensions [Elektronische Daten] [Yvonne Choquet-Bruhat, Piotr Chruściel, José Martín-García] 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. Springer Basel AG, 2011 Choquet-Bruhat Yvonne Académie des Sciences, 23, quai de Conti, 75006, Paris, France aut Chruściel Piotr Gravitational Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria aut Martín-García José Institut d'Astrophysique de Paris and Laboratoire Univers et Théories, UMR 8102, Observatoire de Paris-Meudon, 5, place Jules Janssen, 92195, Meudon, France aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/3(2011-04-01), 419-482 1424-0637 12:3<419 2011 12 23 https://doi.org/10.1007/s00023-011-0076-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0076-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Choquet-Bruhat Yvonne Académie des Sciences, 23, quai de Conti, 75006, Paris, France aut NATIONALLICENCE 700 1- Chruściel Piotr Gravitational Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria aut NATIONALLICENCE 700 1- Martín-García José Institut d'Astrophysique de Paris and Laboratoire Univers et Théories, UMR 8102, Observatoire de Paris-Meudon, 5, place Jules Janssen, 92195, Meudon, France aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/3(2011-04-01), 419-482 1424-0637 12:3<419 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer