  We employ the extended 1+3 orthonormal frame formalism for fluid spacetime
geometries $({\cal M}, {\bf g}, {\bf u})$, which contains the Bianchi field
equations for the Weyl curvature, to derive a 44-D evolution system of
first-order symmetric hyperbolic form for a set of geometrically defined
dynamical field variables. Describing the matter source fields
phenomenologically in terms of a barotropic perfect fluid, the propagation
velocities $v$ (with respect to matter-comoving observers that Fermi-propagate
their spatial reference frames) of disturbances in the matter and the
gravitational field, represented as wavefronts by the characteristic 3-surfaces
of the system, are obtained. In particular, the Weyl curvature is found to
account for two (non-Lorentz-invariant) Coulomb-like characteristic eigenfields
propagating with $v = 0$ and four transverse characteristic eigenfields
propagating with $|v| = 1$, which are well known, and four
(non-Lorentz-invariant) longitudinal characteristic eigenfields propagating
with $|v| = \sfrac{1}{2}$. The implications of this result are discussed in
some detail and a parallel is drawn to the propagation of irregularities in the
matter distribution. In a worked example, we specialise the equations to
cosmological models in locally rotationally symmetric class II and include the
constraints into the set of causally propagating dynamical variables.
