  The conformal flow of metrics [2] has been used to successfully establish a
special case of the Penrose inequality, which yields a lower bound for the
total mass of a spacetime in terms of horizon area. Here we show how to adapt
the conformal flow of metrics, so that it may be applied to the Penrose
inequality for general initial data sets of the Einstein equations. The Penrose
conjecture without the assumption of time symmetry is then reduced to solving a
system of PDE with desirable properties.
