Casimir energy density in closed hyperbolic universes

TL;DR

This paper develops a theoretical framework for calculating Casimir energy density in universes with compact negatively curved spatial sections, extending the concept beyond traditional boundary condition scenarios.

Contribution

It introduces a novel approach to compute Casimir energies in closed hyperbolic universes with scalar fields, expanding the understanding of vacuum energies in curved spacetime.

Findings

Derived formulas for Casimir energy density in hyperbolic geometries

Extended Casimir effect theory to non-boundary conditions in curved spaces

Provided insights into vacuum energy behavior in negatively curved universes

Abstract

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with compact spatial sections of negative spatial curvature.