Extreme Bowen-York initial data

TL;DR

This paper investigates the extreme limit of Bowen-York initial data for spinning black holes, proving the existence of a new solution that exhibits properties similar to extreme Kerr and Reissner-Nordstrom black holes.

Contribution

It demonstrates the existence of a new solution in the extreme limit of Bowen-York data, with a constructive proof showing convergence of a sequence to this solution.

Findings

New solution in the extreme limit of Bowen-York data

Asymptotic end changes from flat to cylindrical

Constructive proof of convergence

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-Nordstrom 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.