Stress-energy tensor of quantized scalar fields in a zero-tidal wormhole

TL;DR

This study examines whether the vacuum stress-energy tensor of a non-minimally coupled scalar field can support a traversable wormhole, identifying parameter regions where the Morris-Thorne conditions are satisfied or violated.

Contribution

It provides the first detailed analysis of the stress-energy tensor in a zero-tidal wormhole for various scalar field parameters, revealing no-go regions for wormhole construction.

Findings

Three parameter regions satisfy Morris-Thorne conditions.

Two mass intervals cannot support traversable wormholes regardless of coupling.

Identifies mass exclusion zones as no-go regimes.

Abstract

To create a static traversable wormhole, exotic matter that meets the Morris-Thorne conditions is required. It is well known that the expectation value of the vacuum stress-energy tensor can violate the null energy condition, and thus has long been considered the best candidate for exotic matter. In this paper, we investigate whether the renormalized stress-energy tensor of a non-minimally coupled massive scalar field in a zero-tidal wormhole can satisfy the Morris-Thorne conditions. Within the Hadamard renormalization framework, we calculate the renormalized stress-energy tensor using the pragmatic mode-sum regularization method recently established by Levi and Ori. By varying the scalar field mass $m_0$ and coupling constant $\xi$, we find that there are three disconnected regions in this two-dimensional parameter space that satisfy the Morris-Thorne conditions. We identify two intervals in the scalar field mass $m_0$, within which the Morris-Thorne conditions cannot be satisfied irrespective of the value of the coupling constant $\xi$. This establishes two mass exclusion regions that constitute a no-go regime for the construction of traversable wormholes.