Binary Systems as Test-beds of Gravity Theories

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We review the general relativistic theory of the motion, and of the timing, of binary systems containing compact objects (neutron stars or black holes). Then we indicate the various ways one can use binary pulsar data to test the strong-field and/or radiative aspects of General Relativity, and of general classes of alternative theories of relativistic gravity.
42 pages, 3 figures, Based on lectures given at the SIGRAV School ``A Century from Einstein Relativity: Probing Gravity Theories in Binary Systems'', Villa Olmo (Como Lake, Italy), 17-21 May 2005. To appear in the Proceedings, edited by M. Colpi et al. (to be published by Springer)

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