Quantum Complex Scalar Field in the Two-Dimensional Spacetime with Closed Timelike Curves and a Time-Machine Problem

TL;DR

This paper investigates the behavior of a quantum complex scalar field in a two-dimensional spacetime with closed timelike curves, showing conditions under which the stress-energy tensor remains regular and potentially violates Hawking's chronology protection conjecture.

Contribution

It provides a specific example of a quantum field configuration that maintains regularity at the chronology horizon, challenging Hawking's conjecture.

Findings

Stress-energy tensor is regular at the chronology horizon for certain parameters.

The example demonstrates a violation of Hawking's chronology protection conjecture.

The study offers insights into quantum field behavior in spacetimes with closed timelike curves.

Abstract

It is considered the quantum complex scalar field which obeys the authomorphic condition in the two-dimensional spacetime with closed timelike curves and the chronology horizon. The renormalized stress-energy tensor is obtained. It is shown that the value of the stress-energy tensor is regular at the chronology horizon for specific authomorphic parameters. Thus the particular example of field configuration is given for which the Hawking's chronology protection conjecture is violated.