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Republication of: Existence theorem for the Einsteinian gravitational field equations in the non-analytic case

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Abstract

This paper was the first announcement of results later elaborated in detail in the more extensive 1952 paper by the same author (now Prof. Yvonne Choquet-Bruhat). They provide a very important theorem on the uniqueness of solutions of the initial value problem for the Einstein equations. This showed that Einstein’s theory shared the property of other physical theories that the evolution of the system is unique given the initial “position” and “velocity”, which here are the Cauchy data for the metric and its derivative.

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Notes

  1. Meeting of 6 February 1950.

  2. Translator’s note: A misprint in this equation has been corrected. Thanks to T. Damour for pointing the mistake out.

References

  1. Stellmacher, K.: Zum Anfangswertproblem der Gravitationsgleichungen. Math. Ann. 115, 136–152 (1938). https://doi.org/10.1007/BF01448933. Translated and republished as Golden Oldie in Gen. Relativ. Gravit. 42, 1769 (2010). https://doi.org/10.1007/s10714-010-0960-1

  2. Sobolev, S.: Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales. Rec. Math. [Mat. Sbornik] N.S. 1(43)(1) 39–72 (1936). http://mi.mathnet.ru/msb5358 and https://zbmath.org/?q=an:0014.05902|62.0568.01

  3. Christianovich, S. Le problème de Cauchy pour les équations non linéaires hyperboliques. Rec. Math. [Mat. Sbornik] N.S. 2(44)(5), 871–899 (1937). http://mi.mathnet.ru/msb5631 and https://zbmath.org/?q=an:0018.12601|63.0469.02

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An editorial note to this paper can be found in this issue at http://doi.org/10.1007/s10714-022-02916-5.

Yvonne Fourès-Bruhat: Théorème d’existence pour les équations de la gravitation einsteinienne dans le cas non analytique. Comptes Rendues Acad. Sci. Paris 230, 618 (1950). https://gallica.bnf.fr/ark:/12148/bpt6k3182n/f618.image

Copyright by Académie des sciences (France).

Translated with permission by M.A.H. MacCallum.

Editorial responsibility: Malcolm A. H. MacCallum, E-mail: m.a.h.maccallum@qmul.ac.uk.

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Fourès-Bruhat, Y. Republication of: Existence theorem for the Einsteinian gravitational field equations in the non-analytic case. Gen Relativ Gravit 54, 35 (2022). https://doi.org/10.1007/s10714-022-02917-4

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  • DOI: https://doi.org/10.1007/s10714-022-02917-4

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