Abstract
General relativity, Einstein's theory of gravity, predicts a universe full of black holes and gravitational waves. The prospects of detecting gravitational waves from inspirals of compact astrophysical objects into supermassive black holes have made it highly important to analyze in detail the gravitational two-body problem. While the two-body problem in Newtonian gravity (the weak-field limit) has a well-defined compact analytic solution, the corresponding problem in general relativity (the strong-field regime) is very complex and cannot be solved analytically. In this paper, we propose to model the two-body problem in general relativity using the analytically solvable model of a ring of particles in orbit around a central black hole. We use our model to calculate the innermost stable circular orbit (ISCO) frequency which characterizes the two-body dynamics. Remarkably, our expression for the characteristic ISCO frequency through linear order in the ring's mass predicts with astonishing accuracy the actual value of this fundamental parameter.
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