On the Quantum Stability of the Time Machine

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.