Hawking's chronology protection conjecture: singularity structure of the quantum stress--energy tensor

TL;DR

This paper calculates the quantum stress-energy tensor in wormhole spacetimes to investigate Hawking's conjecture that quantum effects prevent the formation of time machines, providing detailed analysis and comparisons.

Contribution

It provides an explicit calculation of the vacuum expectation value of the stress-energy tensor in wormhole geometries using point-splitting and Green function techniques.

Findings

Stress-energy tensor diverges near short closed spacelike geodesics.

Results support the idea that quantum effects may prevent time machine formation.

Provides a unified overview of previous calculations in wormhole spacetimes.

Abstract

The recent renaissance of wormhole physics has led to a very disturbing observation: If traversable wormholes exist then it appears to be rather easy to to transform such wormholes into time machines. This extremely disturbing state of affairs has lead Hawking to promulgate his chronology protection conjecture. This paper continues a program begun in an earlier paper [Physical Review {\bf D47}, 554--565 (1993), hepth@xxx/9202090]. An explicit calculation of the vacuum expectation value of the renormalized stress--energy tensor in wormhole spacetimes is presented. Point--splitting techniques are utilized. Particular attention is paid to computation of the Green function [in its Hadamard form], and the structural form of the stress-energy tensor near short closed spacelike geodesics. Detailed comparisons with previous calculations are presented, leading to a pleasingly unified overview of the situation.