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The existence of non-trivial asymptotically flat initial data for vacuum spacetimes. (English) Zbl 0404.53025

53B50 Applications of local differential geometry to the sciences
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
Full Text: DOI
[1] Bourguignon, J.P., Ebin, D., Marsden, J.: Sur le noyau des operateurs pseudo-differential a symbole surjectif et non injectif. C. R. Acad. Sci. Paris A282, 867–870 · Zbl 0323.58020
[2] Cantor, M.: Perfect fluid flows over \(\mathbb{R}\) n with asymptotic conditions. J. Func. Anal.18, 73–84 (1975) · Zbl 0306.58007 · doi:10.1016/0022-1236(75)90030-0
[3] Cantor, M.: Some problems of global analysis on asymptotically simple manifolds. Comp. Math. (to appear) · Zbl 0402.58004
[4] Cantor, M.: Spaces of functions with asymptotic conditions. Indiana U. Math. J.24, 397–902 (1975) · Zbl 0441.46028 · doi:10.1512/iumj.1975.24.24072
[5] Cantor, M., Fischer, A., Marsden, J., O’Murchadha, N., York, J.: The existence of maximal slicings in asymptotically flat spacetimes. Commun. math. Phys.49, 187–190 (1976) · Zbl 0336.53015 · doi:10.1007/BF01608741
[6] Choquet-Bruhat, Y.: Global solutions of the equations of constraints in general relativity on closed manifolds. Symp. Math.XIII, 317–325 (1973) · Zbl 0272.35013
[7] Choquet-Bruhat, Y.: Private correspondence
[8] Choquet-Bruhat, Y.: Probleme des constraintes sur une variete compacte. C. R. Acad. Sci. Paris274, 682–684 (1972) · Zbl 0228.53044
[9] Choquet-Bruhat, Y.: Sous-varietes, ou a courbure constante, de varietes lorentziennes. C. R. Acad. Sci. Paris280, 169–171 (1975) · Zbl 0296.53043
[10] Choquet-Bruhat, Y., Marsden, J.: Solution of the local mass problem in general relativity. C. R. Acad. Sci. Paris282, 609–612 (1976) · Zbl 0364.58013
[11] Fischer, A., Marsden, J.: The manifold of conformally equivalent metrics. Can. J. Math.29, 193–209 (1977) · Zbl 0358.58006 · doi:10.4153/CJM-1977-019-x
[12] Kazden, J., Warner, F.: Scalar curvature and conformal deformation of Riemannian structure. J. Diff. Geom.10, 113–134 (1975) · Zbl 0296.53037
[13] Lang, S.: Introduction to differentiable manifolds. New York: Interscience Publishers 1962 · Zbl 0103.15101
[14] Lichnerowicz, A.: L’integration des equations de la gravitation probleme desn corps. J. Math. Pures Appl.23, 37–63 (1944) · Zbl 0060.44410
[15] Marsden, J.: Applications of global analysis in mathematical physics. Boston: Publish or Perish 1974 · Zbl 0367.58001
[16] Nirenberg, L., Walker, H.: The null space of elliptic partial differential operators in \(\mathbb{R}\) n . J. Math. Anal. Appl.47, 271–301 (1973) · Zbl 0272.35029 · doi:10.1016/0022-247X(73)90138-8
[17] O’Murchadha, N., York, J.: Existence and uniqueness of solutions of the Hamiltonian constraint of general relativity on compact manifolds. J. Math. Phys.14, 1551–1557 (1973) · Zbl 0281.53031 · doi:10.1063/1.1666225
[18] O’Murchadha, N., York, J.: Initial-value problem of general relativity. I. General formulation and physical interpretation. Phys. Rev. D10, 428–436 (1974)
[19] Protter, M., Weinberger, H.: Maximal principles in differential equations. Englewood Cliffs, NJ: Prentice Hall 1967 · Zbl 0153.13602
[20] York, J.W.: Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial value problem of general relativity. J. Math. Phys.14, 456–464 (1973) · Zbl 0259.53014 · doi:10.1063/1.1666338
[21] York, J.W.: Covariant decomposition of symmetric tensors in the theory of gravitation. Ann. Inst. H. Poincare21, 319–332 (1974) · Zbl 0308.53018
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