  This is the second in a series of three papers in which we initiate the study
of very rough solutions to the initial value problem for the Einstein vacuum
equations expressed relative to wave coordinates. By very rough we mean
solutions which cannot be constructed by the classical techniques of energy
estimates and Sobolev inequalities. In this paper we develop the geometric
analysis of the Eikinal equation for microlocalized rough
  Einstein metrics. This is a crucial step in the derivation of the decay
estimates needed in our first paper.
