  We propose a re-formulation of the Einstein evolution equations that cleanly
separates the conformal degrees of freedom and the non-conformal degrees of
freedom with the latter satisfying a first order strongly hyperbolic system.
The conformal degrees of freedom are taken to be determined by the choice of
slicing and the initial data, and are regarded as given functions (along with
the lapse and the shift) in the hyperbolic part of the evolution.
  We find that there is a two parameter family of hyperbolic systems for the
non-conformal degrees of freedom for a given set of trace free variables. The
two parameters are uniquely fixed if we require the system to be ``consistently
trace-free'', i.e., the time derivatives of the trace free variables remains
trace-free to the principal part, even in the presence of constraint violations
due to numerical truncation error. We show that by forming linear combinations
of the trace free variables a conformal hyperbolic system with only physical
characteristic speeds can also be constructed.

General Relativity and Quantum Cosmology