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A covariant multipole formalism for extended test bodies general relativity. (English) Zbl 0124.22201

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[1] M. Mathisson:Acta Phys. Polon.,6, 163 (1937). · Zbl 1188.83018
[2] We have adopted a slightly different notation from that of the papers quoted. For details of the conventions and notation used here, see Sect.2.
[3] J. Weyssenhoff andA. Raabe:Acta Phys. Polon.,9, 7 (1947).
[4] A. Papapetrou:Proc. Roy. Soc.,A 209, 248 (1951).
[5] E. Corinaldesi andA. Papapetrou:Proc. Roy. Soc.,A 209, 259 (1951).
[6] W. Tulczyjew:Acta Phys. Polon.,18, 393 (1959).
[7] B. Tulczyjew andW. Tulczyjew: article inRecent Developments in General Relativity (London, 1962), p. 465.
[8] C. Møller:Comm. Dublin Inst. Adv. Studies, A 5, (1949), has shown that an extended body of positive definite energy density and of given rotational angular momentum about its mass centre must be larger than a certain minimum size.
[9] Loc. cit. ref. (8).
[10] D. Bohm andJ.-P. Vigier:Phys. Rev.,109, 1882 (1958). · Zbl 0082.41602
[11] J. A. Schouten:Ricci-Calculus. An Introduction to Tensor Analysis and its Geometrical Applications, 2nd. ed. (Berlin, 1954).
[12] B. S. DeWitt andR. W. Brehme:Ann. Phys. (N. Y.),9, 220 (1960). See also Chapter II ofJ. L. Synge:Relativity: The General Theory (Amsterdam, 1960). · Zbl 0092.45003
[13] Loc. cit. refs. (12). · Zbl 0092.45003
[14] For a thorough study of various possibilities, seeM. H. L. Pryce:Proc. Roy. Soc.,A 195, 62 (1948), and alsoC. Møller: loc. cit. ref. (8). · Zbl 0032.23605
[15] See Sect.2 and footnotes (12, 14).
[16] Loc. cit. ref. (15).
[17] We here follow the definition of spin given byD. W. Sciama: article inRecent Developments in General Relativity (London, 1962), p. 415. See alsoT. W. B. Kibble:Journ. Math. Phys.,2, 212 (1961). · Zbl 0095.22903
[18] L. Rosenfeld:Mem. Acad. Roy. Belg.,18, 6 (1940). See also ref. (21).
[19] R. Utiyama:Phys. Rev.,101, 1597 (1956). · Zbl 0070.22102
[20] SeeL. Rosenfeld: loc. cit. ref. (22). · Zbl 0070.22102
[21] SeeJ. A. Schouten: loc. cit. ref. (11), Chapter II, Sect.10. · Zbl 0070.22102
[22] For the technique of obtaining these covariant expansions, seeB. S. DeWitt andR. W. Brehme: loc. cit. ref. (12). · Zbl 0070.22102
[23] L. I. Schiff:Phys. Rev. Lett.,4, 215 (1962).
[24] A. Peres:Nuovo Cimento,28, 1091 (1963). · Zbl 0108.41102
[25] See,e.g.,J. L. Synge: loc. cit. ref. (12). · Zbl 0108.41102
[26] SeeB. S. DeWitt andR. W. Brehme: loc. cit. ref. (12). · Zbl 0108.41102
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