  Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70},
104007 (2004)] proposed a new formulation for 3+1 numerical relativity.
Einstein equations result, according to that formalism, in a coupled
elliptic-hyperbolic system. We have carried out a preliminary analysis of the
mathematical structure of that system, in particular focusing on the equations
governing the evolution for the deviation of a conformal metric from a flat
fiducial one. The choice of a Dirac's gauge for the spatial coordinates
guarantees the mathematical characterization of that system as a (strongly)
hyperbolic system of conservation laws. In the presence of boundaries, this
characterization also depends on the boundary conditions for the shift vector
in the elliptic subsystem. This interplay between the hyperbolic and elliptic
parts of the complete evolution system is used to assess the prescription of
inner boundary conditions for the hyperbolic part when using an excision
approach to black hole spacetime evolutions.
