  We investigate the existence and the global causal structure of plane
symmetric spacetimes with weak regularity when the matter consists of an
irrotational perfect fluid with pressure equal to its mass-energy density. Our
theory encompasses the class of weakly regular spacetimes whose metric
coefficients have square-integrable first-order derivatives and whose curvature
must be understood in the sense of distributions. We formulate the
characteristic initial value problem with data posed on two null hypersurfaces
intersecting along a two-plane. Relying on Newman-Penrose's formalism and
expressing our weak regularity conditions in terms of the Newman-Penrose
scalars, we arrive at a fully geometrical formulation in which, along each
initial hypersurface, two scalar fields describing the incoming radiation must
be prescribed. To analyze the future boundary of such a spacetime and identify
its global causal structure, we introduce a gauge that reduces the Einstein
equations to a coupled system of wave equations and ordinary differential
equations for well-chosen unknowns. We prove that, within the weak regularity
class under consideration and for generic initial data, a true spacetime
singularity forms in finite proper time. Our formulation is robust enough so
that propagating discontinuities in the curvature or in the matter variables do
not prevent us from constructing a spacetime whose curvature generically
blows-up on the future boundary. Earlier work on the problem studied here was
restricted to sufficiently regular and vacuum spacetimes.
