The geometry of spacetime with superluminal phenomena

Recent theoretical results show the existence of arbitrary speeds (0 <= v < \infty) solutions of all relativistic wave equations. Some recent experiments confirm the results for sound waves. The question arises naturally: What is the appropriate geometry of spacetime to describe superluminal phenomena? In this paper we present a spacetime model that incorporates the valid results of Relativity Theory and yet describes coherently superluminal phenomena without paradoxes.