Aa. Actor et I. Bender, A PROPERTY OF THE VACUUM STRESS TENSOR IN STATIC CASIMIR THEORY, Journal of physics. A, mathematical and general, 30(19), 1997, pp. 6737-6741
A quantum-field theory defined in any space having arbitrary static ba
ckground structure along some axes but translation invariance along ot
her fee directions (labelled by i) is considered. This system has a re
normalized vacuum-stress tensor T mu upsilon satisfying T-00 = -T-ii.
This relation has nothing to do with T mu upsilon being traceless or d
ivergence free (neither property is assumed).