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In this paper we formulate the relationship between force-freeelectrodynamics and foliations. The background metric, is consideredpredetermined and electrically neutral, but otherwise arbitrary. As it turnsout, solutions to force-free electrodynamics is intimately connected to theexistence of foliations of a spacetime with prescribed properties. We alsoprove a local existence and uniqueness theorem and provide a recipe forconstructing the unique solution/class of solutions when certain conditions aremet. We clarify the theorem with examples. We are also able to also prove asingularity theorem for when non-null solutions approach the null limit. Heretoo, we construct an explicit example to illustrate the singularity theorem.

Force-free Electrodynamics and Foliations in an arbitrary Spacetime