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In the reference $[1]$ the author presented a definition of Stress tensor:

$$ \sigma = 2 \rho \frac{\partial e}{\partial g} \tag{1}$$

In a local chart we have:

$$ \sigma_{ab} = 2 \rho \frac{\partial e}{\partial g_{ab}} \tag{2}$$

So, $\rho$ is the mass density, $e$ the energy density and $g$ the metric tensor.

My question is: what suppose to mean the "metric derivative" $\partial/ \partial g$?

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$[1]$ MARSDEN.J, HUGHES.T.J.R; Mathematical Foundations of Elasticity. page 165. Thm 4.13.

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  • $\begingroup$ Do you understand the equation (2) and just the notation in equation (1) confuses you? Or both equations confuse you? $\endgroup$ – RenatoRenatoRenato Jan 19 at 14:55
  • $\begingroup$ @RenatoRenatoRenato in fact I do not understand the derivative $\partial/ \partial g_{ab}$. Could be something in the context of tensor densities and derivative of metric determinant? $\endgroup$ – M.N.Raia Jan 19 at 14:58

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