Casimir effect in a two dimensional signature changing spacetime

TL;DR

This paper investigates how a change in spacetime signature affects the Casimir effect for scalar fields in a two-dimensional model, revealing destabilization and spectral modifications due to the signature change.

Contribution

It introduces a model of the Casimir effect in a signature-changing spacetime and analyzes the backreaction and algebraic implications of the signature transition.

Findings

Nonzero pressure destabilizes the signature-changing region

Energy spectrum of scalar fields is altered by the signature change

Diffeomorphism algebra's central term is modified

Abstract

We study the Casimir effect for free massless scalar fields propagating on a two-dimensional cylinder with a metric that admits a change of signature from Lorentzian to Euclidean. We obtain a nonzero pressure, on the hypersurfaces of signature change, which destabilizes the signature changing region and so alters the energy spectrum of scalar fields. The modified region and spectrum, themselves, back react on the pressure. Moreover, the central term of diffeomorphism algebra of corresponding infinite conserved charges changes correspondingly.