In this paper we define and construct advanced and retarded Green operators
for the wave operator on spacetimes with low regularity. In order to do so we
require that the spacetime satisfies the condition of generalised hyperbolicity
which is equivalent to well- posedness of the classical inhomogeneous problem
with zero initial data where weak solutions are properly supported. Moreover,
we provide an explicit formula for the kernel of the Green operators in terms
of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a
system of second order ODEs
