  We construct a large class of dynamical vacuum black hole spacetimes whose
exterior geometry asymptotically settles down to a fixed Schwarzschild or Kerr
metric. The construction proceeds by solving a backwards scattering problem for
the Einstein vacuum equations with characteristic data prescribed on the event
horizon and (in the limit) at null infinity. The class admits the full
"functional" degrees of freedom for the vacuum equations, and thus our
solutions will in general possess no geometric or algebraic symmetries. It is
essential, however, for the construction that the scattering data (and the
resulting solution spacetime) converge to stationarity exponentially fast, in
advanced and retarded time, their rate of decay intimately related to the
surface gravity of the event horizon. This can be traced back to the celebrated
redshift effect, which in the context of backwards evolution is seen as a
blueshift.
