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May 8 at 21:27 comment added mike stone I am not sure what "local conservation" means. I usually use that to mean something like $\partial_t \rho+ \nabla \cdot \rho {\bf V}=0$ that implies that a global charge $Q= \int \rho$ is conserved. This not the case here.
May 8 at 17:09 comment added KleinMoretti im sorry to comment on an old question but when you say ""convariant conservation" equations do not imply that any component of the energy or momentum is actually conserved. To get actual conserved quantities you need a symmetry. In particular an isometry associated with a Killing vector field 𝜉𝜇 " you are talking about global conservation right because I thought that ∇𝜇𝑇𝜇𝜈=0. does imply local conservation.
May 28, 2021 at 16:16 history edited mike stone CC BY-SA 4.0
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May 28, 2021 at 16:11 history answered mike stone CC BY-SA 4.0