Maximizing properties of extremal surfaces in general relativity
Brill, Dieter ; Flaherty, Frank
Annales de l'I.H.P. Physique théorique, Tome 29 (1978), p. 335-347 / Harvested from Numdam
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Publié le : 1978-01-01
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     author = {Brill, Dieter and Flaherty, Frank},
     title = {Maximizing properties of extremal surfaces in general relativity},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {29},
     year = {1978},
     pages = {335-347},
     mrnumber = {479299},
     zbl = {0375.53002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1978__28_3_335_0}
}

Brill, Dieter; Flaherty, Frank. Maximizing properties of extremal surfaces in general relativity. Annales de l'I.H.P. Physique théorique, Tome 29 (1978) pp. 335-347. http://gdmltest.u-ga.fr/item/AIHPA_1978__28_3_335_0/

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[2] D. Brill, F. Flaherty, Comm. Math. Phys., t. 50, 1976, p. 157. | MR 459496 | Zbl 0337.53051

[3] E. Heinz, Math. Ann., t. 127, 1954, p. 258 ; M. Miranda, Proc. Symp. Pure Math., XXIII, 1973, p. 1 ; D. Brill, J. Isenberg, to be published. | MR 70013 | Zbl 0055.15303

[4] A.J. Goddard, Ph. D. Thesis, Oxford, 1975. G. R. G. Journal, t. 8, 1977, p. 525.

[5] The operators which we define on the normal bundle would correspond to operators acting on scalars in the usual [1] « 3 + 1 decomposition ». See appendix of [2] for more detail. Among the advantages of using the normal bundle are that e. g. the mean curvature vector is independent of the choice of normal direction, and that the approach can more easily be generalized to hypersurfaces of higher codimension.

[6] See, for example, R. Courant, D. Hilbert, Methods of Mathematical Physics, Vo. II, New York, Wiley, 1962.

[7] M. Morse, The Calculus of Variations in the Large, New York. Amer. Math. Soc., 1934. | JFM 60.0450.01 | Zbl 0011.02802

[8] J. Simons, Ann. Math. (USA), t. 88, 1968, p. 62. | MR 233295 | Zbl 0181.49702

[9] S. Hawking, G. Ellis, The large scale structure of spacetime, Cambridge, University Press, 1973. | MR 424186 | Zbl 0265.53054

[10] F. Tipler, J. Math. Phys., t. 18, 1977, p. 1568. | Zbl 0365.53019

[11] A.H. Taub, Ann. Math. (USA), t. 53, 1951, p. 472; C.W. Misner, A.H. Taub, J. E. T. P., t. 28, 1968, p. 122. | Zbl 0044.22804

[12] D.R. Brill, Phys. Rev. B, t. 133, 1964, p. 845. | MR 161724 | Zbl 0116.44303

[13] We use the convention of earlier publications [11, 12], without a factor 1/2. The « unit » 3-sphere then has radius 2 rather than 1.

[14] A. Lichnerowicz, Problèmes globaux en Mécanique Relativiste, Paris, Herman, 1939 ; Y. Choquet-Bruhat, J. Rat., Mech. Anal., t. 5, 1956, p. 951. | Zbl 0061.47002