Can neutrino vacuum support the wormhole?

TL;DR

This paper calculates the vacuum expectation values of massless fermion stress-energy in a wormhole spacetime, showing neutrino vacuum can violate energy conditions necessary to support the wormhole geometry.

Contribution

It demonstrates that neutrino vacuum naturally violates the averaged weak energy condition in static spherically symmetric wormholes, unlike scalar fields, supporting the wormhole's stability.

Findings

Neutrino vacuum violates the averaged weak energy condition in wormhole spacetimes.

Violation occurs regardless of the specific metric form under slow variation.

Neutrino vacuum behaves similarly to electromagnetic vacuum in this context.

Abstract

The renormalised vacuum expectation values of massless fermion (conventionally call it neutrino) stress-energy tensor are calculated in the static spherically-symmetrical wormhole topology. Consider the case when the derivatives of metric tensor over radial distance are sufficiently small (in the scale of radius) to justify studying a few first orders of quasiclassical (WKB) expansion over derivatives. Then we find that violation of the averaged weak energy condition takes place irrespectively of the detailed form of metric. This is a necessary condition for the neutrino vacuum to be able to support the wormhole geometry. In this respect, neutrino vacuum behaves like electromagnetic one and differs from the conformal scalar vacuum which does not seem to violate energy conditions for slowly varied metric automatically, but requires self-consistent wormhole solution for this.