Useful Computational Formulae

$\displaystyle R_{\beta\nu}$	$\textstyle =$	$\displaystyle \Gamma^{\mu}_{\beta\nu , \mu} - \Gamma^{\mu}_{\beta\mu , \nu} + \... ...Gamma^{\gamma}_{\beta\nu} - \Gamma^{\mu}_{\gamma\nu} \Gamma^{\gamma}_{\beta\mu}$	(20)
$\displaystyle \Gamma^{\gamma}_{\alpha\gamma}$	$\textstyle =$	$\displaystyle \left[\ln \left(\sqrt{-g}\right)\right]_{,\alpha} ~~, ~~~~ g = \left\vert g_{\alpha\beta} \right\vert$	(21)