The two-phase approximation for black hole collisions: Is it robust?

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Recently Abrahams and Cook devised a method of estimating the total radiated energy resulting from collisions of distant black holes by applying Newtonian evolution to the holes up to the point where a common apparent horizon forms around the two black holes and subsequently applying Schwarzschild perturbation techniques. Despite the crudeness of their method, their results for the case of head-on collisions were surprisingly accurate. Here we take advantage of the simple radiated energy formula devised in the close-slow approximation for black hole collisions to test how strongly the Abrahams-Cook result depends on the choice of moment when the method of evolution switches over from Newtonian to general relativistic evolution. We find that their result is robust, not depending strongly on this choice.