  The purpose of this work is to construct asymptotically flat, time symmetric
initial data with an apparent horizon of prescribed intrinsic and extrinsic
geometry. To do this, we use the parabolic partial differential equation for
prescribing scalar curvature. In this equation the horizon geometry is
contained within the freely specifiable part of the metric. This contrasts with
the conformal method in which the geometry of the horizon can only be specified
up to a conformal factor.
