Chronology Protection and Quantized Fields: Complex Automorphic Scalar Field in Misner Space

TL;DR

This paper calculates the stress-energy tensor of a quantized automorphic scalar field in Misner space, revealing conditions under which it remains regular at the chronology horizon, but quantum fluctuations diverge, potentially preventing chronology violation.

Contribution

It provides the first detailed analysis of the automorphic scalar field's stress-energy tensor in Misner space, identifying conditions for regularity and implications for chronology protection.

Findings

Existence of a special automorphic parameter value with regular stress-energy tensor at the horizon

Quantum fluctuations diverge at the horizon, indicating instability

Infinitely growing fluctuations may prevent chronology horizon formation

Abstract

The renormalized stress-energy tensor $\langle T_{\mu\nu}\rangle$ of the quantized complex massless scalar field which obeys the automorphic condition in Misner space is obtained. It is shown that there exists the special value of the automorphic parameter for which $\langle T_{\mu\nu}\rangle$ is regular on the chronology horizon and, so, can not act as a protector of chronology through a back reaction on a spacetime metric. However, it is shown that, at the same time, the value of field square $\langle\phi^2\rangle$, which characterizes the quantum field fluctuations, is divergent on the chronology horizon. The assumption is suggested that the infinitely growing quantum field fluctuations, which appear if a (self)interaction of the scalar field is taken into account, would prevent the chronology horizon formation.