Time Machines Constructed from Anti-de Sitter Space

Abstract

In this paper time machines are constructed from anti-de Sitter space. One is constructed by identifying points related via boost transformations in the covering space of anti-de Sitter space and it is shown that this Misner-like anti-de Sitter space is just the Lorentzian section of the complex space constructed by Li, Xu, and Liu in 1993. The others are constructed by gluing an anti-de Sitter space to a de Sitter space, which could describe an anti-de Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua for a massless conformally coupled scalar field are found for these time machines, whose renormalized stress-energy tensors are finite and solve the semi-classical Einstein equations. The extensions to electromagnetic fields and massless neutrinos are discussed. It is argued that, in order to make the results consistent with Euclidean quantization, a new renormalization procedure for quantum fields in Misner-type spaces (Misner space, Misner-like de Sitter space, and Misner-like anti-de Sitter space) is required. Such a "self-consistent" renormalization procedure is proposed. With this renormalization procedure, self-consistent vacua exist for massless conformally coupling scalar fields, electromagnetic fields, and massless neutrinos in these Misner-type spaces.

17 pages (revtex), 6 figures (4 postscript, 2 gif)

References in corpus (7)

• Can the Universe Create Itself?
• A Self-Consistent Vacuum for Misner Space and the Chronology Protection Conjecture
• Models for Chronology Selection
• Traversable wormholes: the Roman ring
• Inflation in Kaluza-Klein Theory: Relation between the Fine-Structure Constant and the Cosmological Constant
• Must Time Machine Be Unstable against Vacuum Fluctuations?
• Divergences in the Effective Action for Acausal Spacetimes

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