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.