(29a)
$$ \frac{1}{\sqrt{-g}} \frac{\partial \sqrt{-g}}{\partial x_{\sigma}} =
\begin{Bmatrix}\mu \sigma\\\mu\end{Bmatrix} $$
_Divergence of the contravariant four-vector._
Let us multiply (26) with the contravariant fundamental tensor _g_^{μν}
(inner multiplication), then by a transformation of the first member,
the right-hand side takes the form
(A)
$$ \frac{\partial}{\partial x_{\nu}} (g^{\mu\nu} A_{\mu}) - A_{\mu}
\frac{\partial g^{\mu\nu}}{\partial x_{\nu}} - \frac{1}{2}
g^{\tau\alpha} (\frac{\partial g_{\mu\alpha}}{\partial x_{\nu}} +
\frac{\partial g_{ u\alpha}}{\partial x_{\mu}} - \frac{\partial
g_{\mu\nu}}{\partial x_{\alpha}}) g^{\mu\nu} A_{\tau} $$