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Abstract:
The Bowen–York family of spinning black hole initial data depends essentially on one, positive, free parameter. The extreme limit corresponds to making this parameter equal to zero. This choice represents a singular limit for the constraint equations. We prove that in this limit a new solution of the constraint equations is obtained. These initial data have similar properties to the extreme Kerr and Reissner–Nordström black hole initial data. In particular, in this limit one of the asymptotic ends changes from asymptotically flat to cylindrical. The existence proof is constructive, we actually show that a sequence of Bowen–York data converges to the extreme solution.
