  The past quasi-local horizons in vacuum Robinson-Trautman spacetimes are
described. The case of a null (non-expanding) horizon is discussed. It is shown
that the only Robinson-Trautman space-time admitting such a horizon with
sections diffeomorphic to S_2 is the Schwarzschild space-time. Weakening this
condition leads to the horizons of the C-metric. Properties of the hypersurface
r=2m for finite retarded time u are examined.
