Time Machines Constructed from Anti-de Sitter Space

TL;DR

This paper constructs theoretical models of time machines using anti-de Sitter space, analyzes their quantum field properties, and proposes a new renormalization method to ensure consistent quantum vacua.

Contribution

It introduces new constructions of time machines from anti-de Sitter space and develops a self-consistent renormalization procedure for quantum fields in these spacetimes.

Findings

Existence of self-consistent vacua for scalar, electromagnetic, and neutrino fields.

Finite renormalized stress-energy tensors in constructed time machine models.

Proposal of a new renormalization method for quantum fields in Misner-type spaces.

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.