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

Green operators for low regularity spacetimes