  The existence of the initial value constraints means that specifying initial
data for the Einstein equations is non-trivial. The standard method of
constructing initial data in the asymptotically flat case is to choose an
asymptotically flat 3-metric and a transverse-tracefree (TT) tensor on it. One
can find a conformal transformation that maps these data into solutions of the
constraints. In particular, the TT tensor becomes the extrinsic curvature of
the 3-slice. We wish to understand how the physical solution changes as the
free data is changed. In this paper we investigate an especially simple change:
we multiply the TT tensor by a large constant. One might assume that this
corresponds to pumping up the extrinsic curvature in the physical initial data.
Unexpectedly, we show that, while the conformal factor monotonically increases,
the physical extrinsic curvature decreases. The increase in the conformal
factor however means that the physical volume increases in such a way that the
ADM mass become unboundedly large. In turn, the blow-up of the mass combined
with the control we have on the extrinsic curvature allows us to show that
trapped surfaces, i.e., surfaces that are simultaneously future and past
trapped, appear in the physical initial data.
