Quasi-local Casimir energy and vacuum buoyancy in a weak gravitational field

TL;DR

This paper explores the quasi-local energy of Casimir fields in weak gravity, providing an alternative derivation of vacuum buoyancy effects and addressing energy localization issues in curved spacetime.

Contribution

It introduces a quasi-local mass approach to define Casimir energy in a gravitational field, supporting experimental prospects of measuring vacuum energy effects.

Findings

Casimir energy can be associated with a Tolman mass in curved spacetime.

The approach confirms vacuum buoyancy forces on Casimir cavities.

Supports the feasibility of experimentally weighing vacuum energy.

Abstract

Casimir energy in presence of a weak gravitational field is discussed taking into account the issues related to energy and its conservation in a curved background. It is well-known that there are inherent difficulties in defining energy in General Relativity, essentially due to its non-localizability. Using the concept of quasi-local mass and energy, it is shown that it is possible to attribute a Tolman mass to a massless scalar field confined to a Casimir cavity. Such non-local mass coincides - as expected - with the Casimir energy. The present approach offers an alternative derivation of the vacuum buoyancy force acting on a Casimir cavity, confirming the results presented by Calloni {\em et al.} in a series of papers devoted to explore the possibility of experimentally weighting the Casimir vacuum (the so-called Archimedes Experiment).