Must Time Machine Be Unstable against Vacuum Fluctuations ?

In the appearance of absorption material, the quantum vacuum fluctuations of all kinds of fields may be smoothed out and the spacetime with time machine may be stable against vacuum fluctuations. The chronology protection conjecture might break down, and the anti-chronology protection conjecture might hold: There is no law of physics preventing the appearance of closed timelike curves. PACS number(s): 04.20.Gz, 04.62.+v Whether or not the laws of physics permit the existence of closed timelike curves (time machines) is one of important problems in the research field of modern general relativity [1-4]. Hawking has suggested the chronology protection conjecture which states that the laws of physics do not allow the appearance of closed timelike curves [5]. This conjecture was based on the fact that several calculations about the vacuum fluctuations in the spacetime containing closed timelike curves reveal that the renormalized stress-energy tensor always diverges at the Cauchy horizon which separates the region with closed timelike curves from the region without closed causal curves, and also diverges at the polarized hypersurfaces which are nested inside the Cauchy horizon [1,6-10]. Recently Li et al have challenged the chronology protection conjecture [11,12]. They found that in some cases the renormalized stress-energy tensor of vacuum fluctuations might be convergent at the Cauchy horizon and the polarized hypersurfaces. In this paper I will show that ∗Email address: [email protected]