Choptuik Scaling and The Merger Transition

The critical solution in Choptuik scaling is shown to be closely related to the critical solution in the black-string black-hole transition (the merger), through double analytic continuation. This relation is considered for arbitrary space-time dimensions d, and should be tested by numerical simulations. Major consequences include: a suggestion for an alternative, Euclidean, method to obtain the Choptuik constants; an indication that the merger solution exhibits echoing; a prediction for solutions closely related to Choptuik’s to have a critical dimension d = 9, above which the continuous scaling symmetry is restored; the scaling constants, ∆(d), γ(d), are shown to combine naturally to a single complex number; and a method to estimate the scaling constants, together with explicit estimates for one of the cases, based on spontaneous scaling symmetry breaking of cones.