Massive spinor fields in flat spacetimes with non-trivial topology

TL;DR

This paper calculates the vacuum stress-energy tensor for massive spinor fields in various multiply connected flat spacetimes, revealing effects of topology and implications for spacetime stability and chronology protection.

Contribution

It provides the first detailed analysis of spinor vacuum stress tensors in non-trivial topologies, including Mobius strip, Klein bottle, and Misner spacetime.

Findings

Spinor vacuum stress tensor has opposite sign and twice the magnitude of scalar tensor in orientable manifolds.

Topology significantly influences the vacuum stress-energy tensor for spinor fields.

Results have implications for the stability of spacetime and the chronology protection conjecture.

Abstract

The vacuum expectation value of the stress-energy tensor is calculated for spin $1\over 2$ massive fields in several multiply connected flat spacetimes. We examine the physical effects of topology on manifolds such as $R^3 \times S^1$, $R^2\times T^2$, $R^1 \times T^3$, the Mobius strip and the Klein bottle. We find that the spinor vacuum stress tensor has the opposite sign to, and twice the magnitude of, the scalar tensor in orientable manifolds. Extending the above considerations to the case of Misner spacetime, we calculate the vacuum expectation value of spinor stress-energy tensor in this space and discuss its implications for the chronology protection conjecture.