Abstract
Equations of the translational and rotational motion of two bodies possessing intrinsic angular momentum are obtained by the Einstein—Infeld—Hoffmann method in the post-Newtonian approximation. The results agree with the Kerr metric expressed in a harmonic system of coordinates with symmetry of the spatial components of the metric with respect to its indices and with a conservation law for the total angular momentum that is the sum of the orbital and spin angular momenta, and they give the correct passage to the limit to the equation of motion of a test particle with spin.
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References
C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation, W. H. Freeman, San Francisco (1973).
A. Einstein, L. Infeld, and B. Hoffmann,Ann. Math.,39, 65 (1938).
A. Einstein and L. Infeld,Can. J. Math.,1, 209 (1949).
L. D. Landau and E. M. Lifshitz,The Classical Theory of Fields, 3rd ed., Pergamon Press, Oxford (1971).
A. A. Vlasov and A. A. Logunov,Teor. Mat. Fiz.,70, 171 (1987).
V. A. Brumberg,Relativistic Celestial Mechanics [in Russian], Nauka, Moscow (1972).
T. Damour and N. Deruelle,Phys. Lett. A,87, 81 (1981).
A. Papapetrou,Proc. R. Soc., London, Ser. A,209, 248 (1951).
L. L. Schiff,Proc. Nat. Acad. Sci. (USA),46, 871 (1960).
A. P. Ryabushko,Motion of Bodies in the General Theory of Relativity [in Russian], Vyshéishaya Shkola, Minsk (1979).
J. H. Taylor, A. Fowler, and P. M. McCullough,Nature,227, 437 (1979).
I. I. Shapiro, R. D. Reasenberg, J. F. Chandler, and R. W. Babcocle,Phys. Rev. Lett.,61, 2643 (1988).
N. Ashby and B. Sehahid-Saless,Phys. Rev. D,42, 1118 (1990).
Ya. B. Zel'dovich and N. I. Shakura,Pis'ma Astron. Zh.,1, 19 (1975).
Additional information
All-Russia Institute of Experimental Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 1, pp. 123–135, October, 1994.
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Gorbatenko, M.V. Equations of motion of rotating bodies in general relativity in the post-Newtonian approximation. Theor Math Phys 101, 1245–1253 (1994). https://doi.org/10.1007/BF01079262
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DOI: https://doi.org/10.1007/BF01079262