Quantum stability of the time machine

In a number of papers it has been claimed that the time machine is quantum unstable, which manifests itself in the divergence of the vacuum expectation value of the stress-energy tensor $〈\mathrm{T}〉$ near the Cauchy horizon. The expression for $〈\mathrm{T}〉$ was found in these papers on the basis of some specific approach. We show that this approach is untenable in that the above expression, first, is not derived from some more fundamental and undeniable premises, as is claimed, but rather postulated, and second, contains undefined terms, so that one can neither use nor check it. From this we conclude that at the moment there is not a grain of evidence to suggest that the time machine must be unstable. As an illustration we cite a few cases of (two-dimensional) spacetimes containing time machines with $〈\mathrm{T}〉$ bounded near the Cauchy horizon.