On the Quantum Stability of the Time Machine

TL;DR

This paper critiques previous claims of quantum instability in time machines by showing that the key expressions used are unfounded and provides counterexamples where the stress-energy tensor remains bounded.

Contribution

It demonstrates that the commonly used expression for the stress-energy tensor near Cauchy horizons is invalid and offers counterexamples with bounded tensor values.

Findings

Previous approaches are based on unsubstantiated assumptions.

Counterexamples show bounded stress-energy tensor near Cauchy horizons.

Challenges the notion of quantum instability in time machines.

Abstract

In a number of papers it has been claimed that the time machine are quantum unstable, which manifests itself in the divergence of the vacuum expectation value of the stress-energy tensor $\langle{\bf T}\rangle$ near the Cauchy horizon. The expression for $\langle{\bf T}\rangle$ was found in these papers on the basis of some specific approach \cite{Fro,KimT}.\par We show that this approach is untenable in that the above expression firstly is not derived from some more fundamental and undeniable premises, as it is claimed, but rather postulated and secondly contains undefined terms, so that one can neither use nor check it. As a counterexample we cite a few cases of (two-dimensional) spacetimes containing time machines with $\langle{\bf T}\rangle$ bounded near the Cauchy horizon.