  Vacuum asymptotically flat Robinson-Trautman spacetimes are a well known
class of spacetimes exhibiting outgoing gravitational radiation. In this paper
we describe a method of locating the past apparent horizon in these spacetimes,
and discuss the properties of the horizon. We show that the past apparent
horizon is non-timelike, and that its surface area is a decreasing function of
the retarded time. A numerical simulation of the apparent horizon is also
discussed.
