Extremal critical collapse conjecture for vacuum gravity

Consider vacuum gravitational collapse, governed by

$$\operatorname{Ric}(g)=0.$$

The rotating extremal Kerr solution plays the role of extremal Reissner–Nordström. Vacuum extremal-collapse conjecture. Extremal critical collapse occurs in vacuum gravitational collapse, and there exist critical solutions that are isometric to extremal Kerr in the domain of outer communication after sufficiently large advanced time. The conjecture is presented as the vacuum analogue of the charged-scalar statement and remains open.