  We show that for an eikonal limit of gravity in a space-time of any dimension
with a non-vanishing cosmological constant, the Einstein -- Hilbert action
reduces to a boundary action. This boundary action describes the interaction of
shock-waves up to the point of evolution at which the forward light-cone of a
collision meets the boundary of the space-time. The conclusions are quite
general and in particular generalize the previous work of E. and H. Verlinde.
The role of the off-diagonal Einstein action in removing the bulk part of the
action is emphasised. We discuss the sense in which our result is a particular
example of holography and also the relation of our solutions in $AdS$ to those
of Horowitz and Itzhaki.
