  A method for studying the causal structure of space-time evolution systems is
presented. This method, based on a generalization of the well known Riemann
problem, provides intrinsic results which can be interpreted from the
geometrical point of view. A one-parameter family of hyperbolic evolution
systems is presented and the physical relevance of their characteristic speeds
and eigenfields is discussed. The two degrees of freedom corresponding to
gravitational radiation are identified in an intrinsic way, independent of the
space coordinate system. A covariant interpretation of these degrees of freedom
is provided in terms of the geometry of the wave fronts. The requirement of a
consistent geometrical interpretation of the gravitational radiation degrees of
freedom is used to solve the ordering ambiguity that arises when obtaining
first order evolution systems from the second order field equations. This
achievement provides a benchmark which can be used to check both the existing
and future first order hyperbolic formalisms for Numerical Relativity.

General Relativity and Quantum Cosmology