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Stumbles, Sian M.

Hypersurfaces of constant mean extrinsic curvature. (English) Zbl 0472.53063

Ann. Phys. 133, 28-56 (1981).
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Cited in 38 Documents

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C40 Global submanifolds

Keywords:

hypersurfaces; constant mean extrinsic curvature; spacetimes; Robertson- Walker universes

Citations:

Zbl 0332.53035; Zbl 0334.53036
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Full Text: DOI

References:

[1] Eardley, D. M.; Smarr, L., Time functions in numerical relativity, Phys. Rev. D, 19, 2239-2259 (1979)
[2] Marsden, J. E.; Tipler, F. J., Maximal hypersurfaces and foliations of constant mean curvature in general relativity, Bull. Amer. Phys. Soc., 23, 84 (1978)
[3] Choquet-Bruhat, Y.; Fischer, A. E.; Marsden, J. E., Maximal hypersurfaces and positivity of mass, (Proceedings of the Varenna Inter. School of Physics (1976))
[4] Cantor, M.; Fisher, A.; Marsden, J. E.; O’Murchadha, N.; York, J., The existence of maximal slicings in asymptotically flat spacetimes, Comm. Math. Phys., 49, 187-190 (1976) · Zbl 0336.53015
[5] Goddard, A. J., Spacelike hypersurfaces of constant mean extrinsic curvature, (Math. Proc. Camb. Philos. Soc., 82 (1977)), 489-494 · Zbl 0386.53042
[6] Choquet-Bruhat, Y., Maximal submanifolds and submanifolds with constant mean extrinsic curvature, Ann. Scuola Norm. Sup. Pisa., 3, 361-376 (1976) · Zbl 0332.53035
[7] D’Eath, P. D., On the existence of perturbed Robertson-Walker Universes, Ann. Phys. (N.Y.), 98, 237-263 (1976) · Zbl 0334.53036
[8] Sachs, R. K., Asymptotic symmetries in gravitational theory, Phys. Rev., 128, 2851-2864 (1962) · Zbl 0114.21202
[9] Hawking, S. W.; Ellis, G. F.R., (The Large Scale Structure of Spacetime (1973), Cambridge Univ. Press: Cambridge Univ. Press London/New York) · Zbl 0265.53054
[10] Bondi, H.; van der Burg, M. G.J.; Metzner, A. W.K., Gravitational waves in general relativity, (Proc. Roy. Soc. London, 269 (1962)), 21-52 · Zbl 0106.41903
[11] Sachs, R. K., Waves in asymptotically flat spacetime, (Proc. Roy. Soc. London, 270 (1962)), 103-126 · Zbl 0101.43605
[12] Eardley, D. M., (Sources of Gravitational Radiation (1979), Cambridge Univ. Press: Cambridge Univ. Press London/New York) · Zbl 0407.00016
[13] Ladyzhenskaya, O. A.; Ural’tseva, N. N., (Linear and Quasilinear Elliptic Equations (1968), Academic Press: Academic Press New York) · Zbl 0164.13002
[14] Protter, M.; Weinberger, H., (Maximum Principles in Differential Equations (1967), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J) · Zbl 0153.13602
[15] Courant, R.; Hilbert, D., (Methods of Mathematical Physics (1953), Interscience: Interscience New York) · Zbl 0729.00007
[16] Cantor, M., A necessary and sufficient condition for York Data to specify an asymptotically flat spacetime, J. Math. Phys., 20, 1741-1744 (1979) · Zbl 0427.35072
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