The black hole settling-down conjecture

Let $(M,g_{\mu\nu})$ be a strongly asymptotically predictable spacetime, let $\Sigma_t$ be a Cauchy hypersurface for the globally hyperbolic region contained in $M$, and let $B$ denote its black hole region. Suppose

$$B\cap\Sigma_{t'}=\emptyset \quad\text{for all } t'<t,$$

and

$$B\cap\Sigma_{t'}\neq\emptyset \quad\text{for all } t'\geq t.$$

Black hole settling-down conjecture. At $\Sigma_{t'}$, with $t'\gg t$, the spacetime will be described by a stationary metric. This is a dynamical black-hole statement: after black-hole formation, the late-time geometry is expected to settle to stationarity. The supplied text does not state whether the conjecture has been proved or disproved.