Massive scalar field in multiply connected flat spacetimes

TL;DR

This paper calculates the vacuum expectation value of the stress-energy tensor for a massive scalar field in various multiply connected flat spacetimes, revealing how mass influences energy density and potential divergences near chronology horizons.

Contribution

It provides a detailed analysis of how a nonzero mass affects the stress-energy tensor in multiply connected flat spacetimes, including nonchronal regions like Grant space.

Findings

Mass decreases the magnitude of energy density in certain manifolds.

Large mass can prevent divergence of the stress-energy tensor at the chronology horizon.

Massive fields may have limited backreaction on spacetime geometry.

Abstract

The vacuum expectation value of the stress-energy tensor $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ is calculated in several multiply connected flat spacetimes for a massive scalar field with arbitrary curvature coupling. We find that a nonzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as $R^3 \times S^1$, $R^2 \times T^2$, $R^1 \times T^3$, the M\"{o}bius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ remains finite, and the metric backreaction caused by a massive quantized field may not be large enough to significantly change the Grant space geometry.