Comptes Rendus
no. 15-16
Mathematical Physics
A property of light-cones in Einstein's gravity

Presented by: Yvonne Choquet-Bruhat

Yvonne Choquet-Bruhat1; Piotr T. Chruściel2; José M. Martín-García3, 4
1 Académie des Sciences, 23, Quai de Conti, 75270 Paris cedex 06, France
2 Hertford College, Catte Street, Oxford OX1 3BW, UK
3 LUTH, Observatoire de Paris, section de Meudon, 5, place Jules-Janssen, 92195 Meudon cedex, France
4 Institut d'astrophysique de Paris, CNRS, 98bis, boulevard Arago, 75014 Paris, France
Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 971-977.

We prove that the area of cross-sections of future light-cones in a space–time of arbitrary dimension, solution of the Einstein equations with sources satisfying suitable energy conditions, is smaller than the area of corresponding cross-sections for Minkowskian cones, equal only in space–times which are Minkowskian to the future of the light-cone.

On montre que l'aire des sections des cônes de lumière futurs dans un espace–temps de dimension quelconque, solution des équations d'Einstein avec sources obéissant à des conditions d"énergie appropriées, est plus petite que l'aire des sections correspondantes d'un cône Minkowskien, égale seulement dans les espace–temps Minkowskiens dans le futur du cône.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.06.001

Yvonne Choquet-Bruhat 1; Piotr T. Chruściel 2; José M. Martín-García 3, 4

1 Académie des Sciences, 23, Quai de Conti, 75270 Paris cedex 06, France
2 Hertford College, Catte Street, Oxford OX1 3BW, UK
3 LUTH, Observatoire de Paris, section de Meudon, 5, place Jules-Janssen, 92195 Meudon cedex, France
4 Institut d'astrophysique de Paris, CNRS, 98bis, boulevard Arago, 75014 Paris, France 
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     title = {A property of light-cones in {Einstein's} gravity},
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Yvonne Choquet-Bruhat; Piotr T. Chruściel; José M. Martín-García. A property of light-cones in Einstein's gravity. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 971-977. doi : 10.1016/j.crma.2009.06.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.001/

[1] Y. Choquet-Bruhat C. R. Acad. Sci. Paris, Ser. I, 256 (1963), pp. 3971-3973

[2] Y. Choquet-Bruhat, P.T. Chruściel, J.M. Martín-García, in preparation

[3] T. Damour; B. Schmidt J. Math. Phys., 31 (1990), pp. 2441-2453

[4] M. Dossa Ann. Inst. H. Poincaré, 66 (1997), pp. 37-107

[5] G.J. Galloway Ann. H. Poincaré, 1 (2000), pp. 543-567

[6] J.M. Martín-García; xAct Comput. Phys. Comm., 179 (2008), pp. 597-603

[7] A.D. Rendall Proc. Roy. Soc. London A, 427 (1990), pp. 221-239

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