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The existence theory for solutions of the linearized field equations forcausal variational principles is developed. We begin by studying the Cauchyproblem locally in lens-shaped regions, defined as subsets of space-time whichadmit foliations by surface layers satisfying hyperbolicity conditions. Weprove existence of weak solutions and show uniqueness up to vectors in theorthogonal complement of the jets used for testing. The connection between weakand strong solutions is analyzed. Global solutions are constructed byexhausting space-time by lens-shaped regions. We construct advanced andretarded Green's operators and study their properties.

Linearized Fields for Causal Variational Principles: Existence Theory and Causal Structure