Motion of a body in general relativity
1.A. Taub, Proc. Natl. Acad. Sci. (USA) 48, 1570 (1962).
2.In Fact, it is easy to construct counterexamples even to the Newtonian version of this conjecture.
3.See, for example, E. T. Newman, R. Posadas, Phys. Rev. 187, 1784 (1969);
3.E. T. Newman, R. Posadas, J. Math. Phys. 12, 2319 (1971);
3.R. W. Lind, J. Messmer, E. T. Newman, J. Math. Phys. 13, 1884 (1972).
4.E. T. Newman, private communication.
5.See, for example, J. Goldberg, article in Gravitation, an Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), and references therein.
6.See, for example, R. Geroch, J. Math. Phys. 9, 450 (1968);
6.B. Schmidt, J. Rel. Grav. 1, 269 (1971).
7.G. Dixon, Nuovo Cimento 34, 317 (1964).
8.Such fields exist. First note that the right‐hand side of (1) defines a linear mapping from the ten‐dimensional vector space of Killing fields on M to the reals. Since a Killing field is completely determined by its value, together with the value of its derivative, at any one point, there exists, for each point p, a and at p such that (1) holds with the left‐hand side evaluated at p.
9.E. Fermi, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 31, 21, 51 (1922).
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