Mathematical problems in general relativity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 40 (1985) no. 6 Cet article a éte moissonné depuis la source Math-Net.Ru

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     author = {Y. Choquet-Bruhat},
     title = {Mathematical problems in general relativity},
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}
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Y. Choquet-Bruhat. Mathematical problems in general relativity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 40 (1985) no. 6. http://geodesic.mathdoc.fr/item/RM_1985_40_6_a22/

[1] Arnowitt R., Deser S., Misner C., Gravitation, an Introduction to Current Research, eds. L. Witten, Wiley, New York, 1962, 227 | MR

[2] Bartnik R., Asymptotic behaviour of mass and space time geometry, Lect. Notes in Physics, eds. F. Flaherty, Springer-Verlag, 1984 | MR | Zbl

[3] Brill D., Deser S., “Variational methods and positive energy in general relativity”, Ann. Phys., 50:3 (1968), 548–570 | DOI | MR

[4] Cagnac F., “Probleme de Cauchy sur un conoide caracteristique”, Ann. Fac. Sci. Toulouse Math., 2:1 (1980), 11–19 | MR | Zbl

[5] Carter B., Einstein Centenary Survey, eds. Hawking and Israël, Cambridge Univ. Press, 1978 | Zbl

[6] Choquet-Bruhat Y., “Construction de solutions radiatives approachees des equations d'Einstein”, Comm. Math. Phys., 12:1 (1969), 16–35 | DOI | MR

[7] Choquet-Bruhat Y., De Witt-Morette C., Dillard-Bleick M., Analysis Manifolds and Physics, 2nd rev. ed, North-Holland, Amsterdam, 1982 | MR | Zbl

[8] Choquet-Bruhat Y., Marsden J., “Solution of the local mass problem in general relativity”, Comm. Math. Phys., 51:3 (1976), 283–296 | DOI | MR | Zbl

[9] Choquet-Bruhat Y., Christodoulou D., “Elliptic systems in $H_{s,\sigma}$ spaces on manifolds which are euclidean at infinity”, Acta Matematica, 146:2 (1981), 129–150 | DOI | MR | Zbl

[10] Choquet-Bruhat Y., York J. M., “The Cauchy problem”, General relativity and gravitation, Plenum, eds. A. Held, 1980 | MR

[11] Choquet-Bruhat Y., Fischer A., Marsden J., Isolated gravitatig systems in general relativity, eds. J. Ehler, North-Holland, Amsterdam, 1979

[12] Choquet-Bruhat Y., Gravitation, an introduction to current research, eds. L. Witten, J. Wiley, 1962 | MR

[13] Choquet-Bruhat Y., Proceeding of the Second Marcel Grossman meeting (Trieste, 1979), North-Holland, 1982 | MR | Zbl

[14] Choquet-Bruhat Y. in book in the hohour of I. Robinson (to appear)

[15] Choquet-Bruhat Y., Battelle Rencontres 1967, eds. C. De Witt and J. Wheeler, Benjamin, 1968 | MR

[16] Choquet-Bruhat Y., Geroch R., “Global aspects of the Cauchy problem in general relativity”, Comm. Math. Phys., 14 (1969), 329 | DOI | MR | Zbl

[17] Choquet-Bruhat Y., “$C^\infty$-solutions of hyperbolic nonlinear equations”, Gen. Relativ. Gravit., 2 (1972), 359 | DOI | MR

[18] Choquet-Bruhat Y., “Positive energy theorems”, General relativity groups and topology, eds. B. De Witt, North-Holland, 1984 | MR

[19] Christodoulou D., O'Murchadha N., “The boost problem in general relativity”, Comm. Math. Phys., 80:1 (1981), 271–300 | DOI | MR | Zbl

[20] Christodoulou D., “The boost problem for weakly coupled quasilinear hyperbolic systems of the second order”, J. Math. pures et appl., 60, f.l (1981), 99–130 | MR | Zbl

[21] Christodoulou D., “Violation of cosmic censorship in the gravitional collapse of a dust cloud”, Comm. Math. Phys., 93:2 (1984), 171–196 | DOI | MR

[22] Christodoulou D., Preprint, Syracuse, 1984

[23] Clark C., General relativity and gravitation, Plenum, eds. Held, 1980

[24] Brill D., Deser S., Faddeev L. D., “Sign of gravitational energy”, Phys. Lett., 26A:11 (1968), 538–539

[25] Deser S., Teitelboim C., “Supergravity has positive energy”, Phys. Rev. Lett., 39:5 (1977), 249–251 | DOI

[26] Deser S., “Positive classical gravitational energy from classical supergravity”, Phys. Rev. D, 27:2, 2805–2808 | DOI | MR

[27] Fischer A., Marsden J., Isolated gravitating systems in general relativity, eds. Ehlers, North-Holland, 1979 | MR

[28] Fisher A., Marsden Dzh., “Problema nachalnykh dannykh i dinamicheskaya formulirovka obschei teorii otnositelnosti”, Obschaya teoriya otnositelnosti, eds. S. Khoking, V. Izrael, Mir, M., 1983

[29] Fischer A., Marsden J., Moncrief V., “The structure of the space of solutions of Einstein's equations. I. One killing field”, sect. A, Ann. Inst. Henri Poincare, 33:2 (1980), 147–194 | MR | Zbl

[30] Friedrich H., “On the regular and the asymptotic characteristic initial value problem for Einstein's vacuum field equations”, Proc. Roy. Soc. London, ser. A, 375:1761 (1981), 169–184 | DOI | MR | Zbl

[31] Geroch R., “Domain of dependence”, J. Math., Phys., 11:2 (1970), 437–439 | DOI | MR

[32] Geroch R., Horowitz G., Einstein centenary survey, eds. Hawking and Israël, Cambridge Univ. Press, 1979 | MR | Zbl

[33] Khoking S., Ellis D., Krupnomasshtabnaya struktura prostranstva-vremeni, Mir, M., 1976

[34] Horowitz G., Strominger W., “Witten's expression for gravitational energy”, Phys. Rev. D, 27:12 (1983), 2793–2804 | DOI | MR

[35] Hull W., DAMTP preprint, Univ. of Cambridge, 1983

[36] Israël W., Stewart J., Einstein Centenary survey, eds. Hawking and Israël, Cambridge Univ. Press, 1979 | MR

[37] Kramer D., Stephani H., Mac Callum M., Hert E., Exact solutions of Einstein's field equations, eds. Schmutzer, V.E.B., Berlin, 1980; Tochnye resheniya uravnenii Einshteina, eds. E. Shmuttsera, Energoizdat, M., 1982) | MR

[38] Leray J., Hyperbolic differential equations, mimeographes IAS Princeton, 1952 ; Lere Zh., Giperbolicheskie differentsialnye uravneniya, Mir, M., 1984) | MR | MR

[39] Lichnerowicz A., Theories relativistes de la gravitation et de l'electromagnetisme, Masson, 1955 | Zbl

[40] Isenberg J., Moncrief V., “The existence of constant mean curvature foliations of Gowdy 3-torus specetimes”, Comm. Math. Phys., 86:4 (1982), 485–494 | DOI | MR

[41] Moncrief V., “The space of (generalized) Taub-NUT spacetimes”, J. of geometry and phisics, 1:1 (1984), 107–130 | DOI | MR | Zbl

[42] Nester J., “A new gravitational energy expression with a simple positivity proof”, Phys. Lett., 83A:6 (1981), 241–242 | MR

[43] Parker T., Taubes T., “On Witten's proof of the positive energy theorem”, Comm. Math. Phys., 84:3 (1982), 223–238 | DOI | MR | Zbl

[44] Penrouz R., “Singulyarnosti i asimmetriya vo vremeni”, Obschaya teoriya otnositelnosti, eds. S. Khoking, V. Izrael, Mir, M., 1983

[45] Reula O., “Existence theorem for solutions of Witten's equation and non negativity of total mass”, J. Math. Phys., 23:5 (1982), 810–814 | DOI | MR | Zbl

[46] Schoen R., Yau S.-T., “On the proof of the positive mass conjecture in general relativity”, Comm. Math. Phys., 65:1 (1979), 45–76 | DOI | MR | Zbl

[47] Schoen R., Yau S.-T., “Proof of the positive mass theorem. II”, Comm. Math. Phys., 79:3 (1981), 231–260 | DOI | MR | Zbl

[48] Schoen R., Yau S.-T., “The energy and the linear momentum of spacetimes in general relativity”, Comm. Math. Phys., 79:1 (1981), 47–52 | DOI | MR

[49] Witten E., “A new proof of the positive energy theorem”, Comm. Math. Phys., 80:3 (1981), 381–402 | DOI | MR | Zbl

[50] Ashtekar A., Horowitz G., “Energy-momentum of isolated systems cannot be null”, Phys. Lett., 89A:4, 181–184 | MR

[51] Gibbons W., Hawking S. W., Horowitz G. T., Perry M. J., “Positive mass theorems for black holes”, Comm. Math. Phys., 88:3 (1983), 295–308 | DOI | MR

[52] Horowitz G., Asymptotic behaviour of mass and space time geometry, Lect. Notes in Physics, no. 202, 1984

[53] Taub A. in Ann. de l'Institut Henri Poincare (to appear)

[54] Choquet-Bruhat Y., Ruggeri T., “Hyperbolicity of the $3+1$ system of Einstein equations”, Comm. Math. Phys., 89:2 (1983), 269–276 | DOI | MR

[55] Mizner Ch., Torn K., Uiler Dzh., Gravitatsiya, t. 1, 2, 3, Mir, M., 1977

[56] Penrouz R., Struktura prostranstva-vremeni, Mir, M., 1972 | MR