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 [Phys. Rev. D 48, 4735 (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 semiclassical 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 coupled scalar fields, electromagnetic fields, and massless neutrinos in these Misner-type spaces.