Abstract
Although it has been known for a long time that causality violation is not a priori ruled out by General Relativity, its investigation became a concerted effort only about a decade ago. This may have been prompted by the realization that if a “wormhole” could be created it would be possible to build a “time machine” (a space-time with compact achronal region). It has turned out to be surprisingly difficult to prove the physical impossibility of such space-times (as most relativists would want to have it). The most convincing argument in this direction rests on the semiclassical instability of the Cauchy horizon (i.e. a divergent 〈T μν〉 at the boundary of the achronal region) and underlies the “chronology protection conjecture” of Hawking (1992). But even if this is taken for granted, microscopic closed time-like curves may be allowed in quantum gravity. One is then led to consider as a tractable model problem quantum field theory on a background space-time with closed time-like curves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hawking, S.W. (1992): Phys. Rev. D46, 603
Kay, B.S., Radzikowski, M.J., Wald, R.M. (1997): Commun. Math. Phys. 183, 533
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rumpf, H. (2000). Quantum Field Theory in Non-globally Hyperbolic Space-Times. In: Gausterer, H., Pittner, L., Grosse, H. (eds) Geometry and Quantum Physics. Lecture Notes in Physics, vol 543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46552-9_24
Download citation
DOI: https://doi.org/10.1007/3-540-46552-9_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67112-1
Online ISBN: 978-3-540-46552-2
eBook Packages: Springer Book Archive