The vacuum third law of black hole thermodynamics

Let $g$ be a spacetime metric satisfying the vacuum Einstein equations

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

A Cauchy datum is regular and one-ended when it is regular and has one asymptotically flat end, and gravitational collapse means that it forms a black hole to the future of the initial data. The vacuum third law of black hole thermodynamics. There exist regular one-ended Cauchy data for the Einstein vacuum equations which undergo gravitational collapse and form an exactly Schwarzschild apparent horizon, only for the spacetime to form an exactly extremal Kerr event horizon at a later advanced time. In particular, already in vacuum, the third law of black hole thermodynamics is false. This is presented as a proposed vacuum analogue of the counterexample and is not established by the surrounding text.