Misner Space as a Prototype for Almost Any Pathology

Abstract

Abstract Misner space (i.e. Minkowski spacetime with identification under a boost) is a remarkably rich prototype for a variety of pathologies in the structure of spacetime—some of which may actually occur in the real Universe. The following examples are discussed in some detail: traversable wormholes, violation of the averaged null energy condition, chronology horizons (both compactly and noncompactly generated) at which closed timelike curves are created, classical and quantum instabilities of chronology horizons, and chronology protection. Introduction In August 1965, at the Fourth Summer Seminar on Applied Mathematics at Cornell University, Charles Misner gave a lecture titled “Taub-NUT space as a counterexample to almost anything” [Mis67]. Near the end of his lecture, Misner introduced an exceedingly simple spacetime that shares some of Taub-NUT's pathological properties. This spacetime has come to be called Misner space . Twenty-three years later, when I became intrigued by the question of whether the laws of physics forbid traversable wormholes and closed timelike curves, and if so, by what physical mechanism the laws prevent them from arising, Bob Wald and Robert Geroch reminded me of Misner space and its relevance to these issues. Since then, I and others probing these issues have found Misner space and its variations to be fertile testing grounds and powerful computational tools. In this paper, I shall describe the remarkable pathologies that Misner space encompasses, and what we have learned about wormholes and closed timelike curves with the aid of Misner space. My discussion will be quite elementary, requiring little more than a basic understanding of special relativity.