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The two-body problem in general relativity: A new approach

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Lettere al Nuovo Cimento (1971-1985)

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Footnotes

  1. A. S. Eddington:The Mathematical Theory of Relativity (Cambridge, 1965), p. 251.

  2. A. Einstein:Sitzber. Preuss. Akad. Phys.-Math. Kl., 688 (1916). See alsoL. D. Landau andE. M. Lifshitz:The Classical Theory of Fields, Third revised English edition (Reading, Mass., 1971), p. 325.

  3. SeeW. B. Bonnor:Brit. Journ. Appl. Phys.,14, 555 (1963)

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  4. SeeL. Infeld andR. Michalska-Trautman:Ann. of Phys.,55, 561, 576 (1969).

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  5. A. Papapetrou:Ann. der Phys.,20, 399 (1957);1, 185 (1958);2, 87 (1958).

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  6. Colloque International «Ondes et radiations gravitationnelles» Paris, June 1973

  7. H. E. J. Curzon:Proc. Lond. Math. Soc.,23, 477 (1924). See alsoJ. L. Synge:Relativity: the General Theory, Chap. VIII (Amsterdam, 1960).

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  8. H. Bondi:Rev. Mod. Phys.,29, 423 (1957).

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  9. R. Bach andH. Weyl:Math. Zeits.,43, 134 (1922). ∨ and γ of eq. (3) are solutions of the vacuum field equations and are thus not applicable in the region of stress between the two masses.

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  10. SeeN. Rosen andH. Shamir:Rev. Mod. Phys.,29, 429 (1957);W. B. Bonnor:Phil. Trans. Roy. Soc.,251, 233 (1959) for important foundation work on axially symmetric time-dependent fields.

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  11. FromBach andWeyl (ref. (9) the equilibrium-sustaining force is – γ(r ≃ 0)/4G ≃Gm 2/4α2. Hence, the stress has been completely removed in the second-order field equations (4) and no further contribution is required to these third (or any higher)-order equations.

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Author notes

  1. F. I. Cooperstock (Canada-France Scientific-Exchange Visitor)

    Present address: Department of Physics, University of Victoria, Victoria, B. C.

Authors and Affiliations

  1. Laboratoire de Physique Théorique, Institut Henri Poincaré, Paris

    F. I. Cooperstock (Canada-France Scientific-Exchange Visitor)

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  1. F. I. Cooperstock
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Supported by the National Research Council of Canada, Grants A54340, T0624.

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Cooperstock, F.I. The two-body problem in general relativity: A new approach. Lett. Nuovo Cimento 10, 555–560 (1974). https://doi.org/10.1007/BF02784781

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