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Forums
Physics
Special and General Relativity
Deriving Einstein Equations: Questions on Linearity & Symmetry
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[QUOTE="Decimal, post: 6017176, member: 625746"] Yeah I should have been clearer here. The way my book introduced Einsteins proposal uses the formula for Newtonian gravity $$ \nabla^2 \Phi = 4\pi G \rho$$ and the linearized metric for a weak gravitational field: $$g_{00} = (1+\frac{2\Phi}{c^2})$$ Combining these equations with ##T_{00} = \rho c^2## for a perfect fluid one can derive: $$ \nabla^2 g_{00} = \frac{8\pi G}{c^4} T_{00}$$ Now Einsteins proposal would suggest that ## K_{\mu \nu} ## is somehow related to ## \nabla^2 g_{\mu \nu}##. This is why I said the ##K## tensor is related to the laplacian of the metric. I understand the Laplacian usually doesn't appear in GR. I think this relation might have something to do with the linear second order derivatives. The laplacian is obviously linear in second derivatives, so is that why ##K_{\mu \nu}## should be as well? [/QUOTE]
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Physics
Special and General Relativity
Deriving Einstein Equations: Questions on Linearity & Symmetry
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