The two-body problem in geometrodynamics

My research group works mainly on two-body astrophysical problems using the theory of general relativity. During a recent discussion, I was reminded by my advisor that the two-body problem in general relativity has never been solved analytically. As such, the advent of numerical relativity was an effort in itself to tackle this problem – to describe the bodies in the framework of general relativity and solve the Einstein field equations by virtue of casting them as a finite-differenced initial value problem, entailing the employment of a finite hypersurface to characterize the initial conditions with suitable boundary conditions. However, to be mindful of the historicity of this problem, I dug out this paper:

The Two-Body Problem in Geometrodynamics, S. G. Hahn and R. W. Lindquist, Ann. Phys. (N. Y.) 29 (1964), 304.

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~ by musafiremes on November 29, 2007.

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