Vacuum Schwarzschild-to-Kerr characteristic gluing conjecture

Let $M_i$ and $R_i$ be the mass and radius of a Schwarzschild symmetry sphere. Let $R_f$ be the radius of a non-antitrapped Kerr coordinate sphere in a Kerr solution with mass $M_f$ and specific angular momentum $a_f$, where

$$R_f\gg R_i,\qquad M_f\gg M_i,\qquad 0\leq |a_f|\leq M_f.$$

Vacuum Schwarzschild-to-Kerr characteristic gluing conjecture. The Schwarzschild symmetry sphere of mass $M_i$ and radius $R_i$ can be characteristically glued to any such non-antitrapped Kerr coordinate sphere.

If true, this would provide a vacuum mechanism for spinning Schwarzschild up to extremality and would imply that the third law of black hole thermodynamics is false already for the Einstein vacuum equations. The conjecture is presented as a proposed generalization of the authors’ previous characteristic gluing construction and remains open.