= Newtonian gravitational stress tensor
{c}
{title2=$T_{ij}$}
For a <Newtonian gravitational potential> obeying the <Poisson equation for Newtonian gravity>, define $T_{ij}=[\partial_i\Phi\partial_j\Phi-\delta_{ij}|\nabla\Phi|^2/2]/(4\pi G)$. Commutation of mixed <partial derivatives> gives $\partial_jT_{ij}=\rho\partial_i\Phi$. Thus the gravitational force density can be put in conservative form as $-\partial_jT_{ij}$. The sign is chosen so that $T_{ij}$ is added to the momentum flux; reversing the stress convention reverses the divergence sign.
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