Volumetric WCC for future incomplete causal geodesics

Let $(M,g)$ be a spacetime and define

$$\mathcal{B}:=\{x\in M\mid \operatorname{vol}_g(I^+(x))<\infty\}.$$

A causal geodesic is future incomplete if it cannot be extended to arbitrarily large future parameter values. Volumetric WCC. In a generic physically realistic spacetime, every future incomplete causal geodesic enters the set $\mathcal{B}$. This is proposed as a volume formulation of Weak Cosmic Censorship: future incomplete causal geodesics should eventually lie in the interior of a volume black hole, and hence be hidden by its event horizon. The source presents this as an ambitious programme and gives no resolution.