Hello,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Conserved Gravitational Charges and Question on Equal Divergences

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**