Geodesic
An existence theorem for the Cauchy problem on the light-cone for the vacuum Einstein equations with near-round analytic data
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 115-138

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A class of characteristic general relativistic initial data satisfying a near-roundness condition at the tip of a light-cone is introduced. It is shown that for any such analytic data there exists a corresponding solution of the vacuum Einstein equations defined in a future neighborhood of the vertex.
Keywords: characteristic Cauchy problem on a light-cone, vacuum Einstein equations. 
@article{UZKU_2011_153_3_a11,
     author = {Y. Choquet-Bruhat and P. T. Chru\'sciel and J. M. Mart{\'\i}n-Garc{\'\i}a},
     title = {An existence theorem for the {Cauchy} problem on the light-cone for the vacuum {Einstein} equations with near-round analytic data},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {115--138},
     publisher = {mathdoc},
     volume = {153},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a11/}
}
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Y. Choquet-Bruhat; P. T. Chruściel; J. M. Martín-García. An existence theorem for the Cauchy problem on the light-cone for the vacuum Einstein equations with near-round analytic data. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 115-138. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a11/