Vacuum polarization of a scalar field in wormhole spacetimes

TL;DR

This paper derives an analytical approximation for the vacuum expectation value of the squared scalar field in static spherically symmetric wormhole spacetimes, considering both massive and massless cases with arbitrary curvature coupling.

Contribution

It provides the first analytical approximation of <φ²> in wormhole geometries for various scalar field parameters and coupling, expanding understanding of quantum effects in such spacetimes.

Findings

Analytical expression for <φ²> in wormhole spacetimes.

Applicability to both massive and massless scalar fields.

Inclusion of arbitrary curvature coupling ξ.

Abstract

An analitical approximation of $<\phi^2>$ for a scalar field in a static spherically symmetric wormhole spacetime is obtained. The scalar field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state.