Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 311 1 b i Solution Created 2026-10-03 Updated 2026-10-06
The common axial Killing vector field fixes the same sign convention for both spins. Initial rest and alignment of the separation with the symmetry axis give no orbital angular momentum. At large separation, the total axial charge is therefore . Since axisymmetric radiation carries no axial angular momentum, all of this charge remains in the remnant after the radiation has escaped and the exterior has settled:Here the spins are signed quantities about the same axis, not their magnitudes. The conclusion assumes the exact axisymmetry stipulated throughout the merger and no remaining exterior matter carrying angular momentum; the final stationary vacuum remnant is a Kerr black hole under the usual uniqueness hypotheses.