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arXiv · 2607.06695

Geometry-induced Casimir response in a helicoidal spacetime

Edilberto O. Silva
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Abstract

We investigate the Casimir response of a massive scalar field in a torsionless helicoidal spacetime with Levi-Civita connection. The background is ultrastatic and curved, with scalar curvature \(R=-2\Omega^2\), and its off-diagonal metric component induces a geometric coupling between angular and axial quantum numbers. We show that individual modes exhibit a linear helicoidal splitting, whereas the linear contribution cancels in the nonchiral vacuum sum. The leading Casimir correction is therefore quadratic in the twist and defines a helicoidal vacuum susceptibility after local ultraviolet subtractions. For a cylindrical Dirichlet cavity, we compute this scheme-defined susceptibility and the associated correction to the radial Casimir force. The results identify torsionless helicoidal geometry as a controlled setting in which mode-level chirality produces a finite quadratic response of vacuum fluctuations.

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Edilberto O. Silva. 2026-07-07. Geometry-induced Casimir response in a helicoidal spacetime. https://arxiv.org/abs/2607.06695

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