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I am working on a project but I stuck at a point. I found that divergence of two objects are equal

[itex]\nabla_{a}J^{ab}=\nabla_{a}K^{ab}[/itex]. They are also equal to zero, so I try to construct conserved quantities out of them by using Stoke's theorem.

[itex]\int_{M}\nabla_{a}J^{ab}d^{d-1}x=\int_{\partial{M}}J^{ab}d\Sigma_{a}=0[/itex]

Assuming that the J vanishes sufficiently fast at spatial infinity we can find

[itex]\int_{\Sigma_{1}}J^{ab}\sqrt{-g}d^{d-2}x=\int_{\Sigma_{2}} J^{ab}\sqrt{-g}d^{d-2}x[/itex]

meaning that [itex]J^{ab}[/itex] is a conserved quantity. Same holds for [itex]K^{ab}[/itex] too. However I wonder that what is the relation between the two charges. Since the divergence of both tensor are equal to each other(at this point I should note that, I can transform them to each other only by using Bianchi identities without adding 0's), what can I say about their original forms. Any help would be appreciated. Thanks.

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# Conserved Gravitational Charges and Question on Equal Divergences

Can you offer guidance or do you also need help?

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