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).

中文翻译：

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弱引力场中的准局域 Casimir 能量和真空浮力

考虑到与能量及其在弯曲背景中的守恒相关的问题，讨论了存在弱引力场时的卡西米尔能量。众所周知，广义相对论中定义能量存在固有的困难，主要是由于其不可定位性。使用准局部质量和能量的概念，表明可以将托尔曼质量归因于限制在卡西米尔腔内的无质量标量场。这种非局部质量与卡西米尔能量一致——正如预期的那样。本方法提供了作用在 Casimir 腔上的真空浮力的另一种推导，证实了 Calloni {\em 等人}在一系列致力于探索实验加权 Casimir 真空的可能性的论文中提出的结果（所以——称为阿基米德实验）。