Abstract
We consider the problem of the gravitational interaction of two compact bodies (neutron stars or black holes). We outline a new method where one matches an “external” gravitational field, obtained by iterating a Post Minkowskian Approximation scheme, to the field near each compact body. Equations of motion for each body are derived from the vacuum field equations by means of an Einstein-Infeld-Hoffmann-Kerr-like approach simplified by the use of complex analytic continuation. Because of the “no incoming radiation” condition incorporated in the Post Minkowskian Approximation scheme these equations of motion have a retarded functional form. A slow motion expansion allows one to transform these equations into ordinary differential equations up to the second-and-a-half-Post-Newtonian order. Solving the latter equations, with the help of a second-Post-Newtonian generalized Lagrangian, we find a secular acceleration of the mean orbital longitude of each member of a gravitationally bound binary system. This kinematical behaviour agrees with the phenomena observed in the Hulse-Taylor pulsar: PSR 1913+16.
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Damour, T. (1984). The Motion of Compact Bodies and Gravitational Radiation. In: Bertotti, B., de Felice, F., Pascolini, A. (eds) General Relativity and Gravitation. Fundamental Theories of Physics, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6469-3_7
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