Black hole mergers and unstable circular orbits

We describe recent numerical simulations of the merger of a class of equal mass, non-spinning, eccentric binary black hole systems in general relativity. We show that with appropriate fine tuning of the initial conditions one can reach a region of parameter space we denote the threshold of immediate merger. Here, the binary enters a phase of close interaction in a near-circular orbit, stays there for an amount of time proportional to the logarithmic distance from the threshold in parameter space, then either separates or merges to form a single Kerr black hole. To gain a better understanding of this phenomenon, we study an analogous problem in the evolution of equatorial geodesics about a central Kerr black hole. A similar threshold of capture exists for appropriate classes of initial conditions, and tuning to threshold the geodesics approach one of the unstable circular geodesics of the Kerr spacetime. Remarkably, with a natural mapping of the parameters of the geodesic to that of the equal mass system, the scaling exponents describing the whirl phase of each system turn out to be quite similar. Armed with this lone piece of evidence that an approximate correspondence might exist between near-threshold evolution of geodesics and generic binary mergers, we illustrate how this information can be used to estimate the cross section and energy emitted in the ultra-relativistic black hole scattering problem. This could eventually be of use in providing estimates for the related problem of parton collisions at the large hadron collider in extra dimension scenarios where black holes are produced.