2024-03-04   32191

Relationship Between the Stress-Energy Tensors

Article 49705 showed that in flat spacetime, translation invariance implies a conservation law of the form ∂a TCab = 0. Article 37501 showed that in general relativity, the equation of motion for the metric field involves a different quantity THab that also satisfies the conservation law ∂a THab=0 when spacetime is flat. Both TCab and THab are called the stress-energy tensor (the subscripts C and H stand for canonical and Hilbert, respectively), but their definitions are different: they are generally not equal to each other, and they are conserved for what appear to be different reasons. After reviewing those reasons, this article illustrates how an ambiguity in the definition of TCab can be exploited to make it "practically" the same as THab.

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www.cphysics.org updated 2024-04-08