The evaluation of Casimir energies in curved background spacetimes is an essential ingredient to study the stability of traversable wormholes. In practice one has to calculate the contribution of the transverse-traceless component of the metric perturbation on a curved spacetime background. This implies the study of an eigenvalue equation involving a modified form of the Lichnerowicz operator. For arbitrary background spacetimes, however, such an operator does not display transverse-traceless properties, a fact that impedes the determination of the eigenvalues. Against this background, we show that the problem can be circumvented. Casimir energies can be calculated by gauging the original form of the modified Lichnerowicz operator into a transverse-traceless one.

弯曲背景时空中卡西米尔能量的评估是研究可穿越虫洞稳定性的重要组成部分。在实践中，必须计算度量扰动的横向无迹分量对弯曲时空背景的贡献。这意味着研究涉及 Lichnerowicz 算子的修改形式的特征值方程。然而，对于任意背景时空，这样的算子不显示横向无迹特性，这一事实阻碍了特征值的确定。在此背景下，我们表明可以规避该问题。卡西米尔能量可以通过将修改后的 Lichnerowicz 算子的原始形式测量为横向无迹算子来计算。