Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 38C / c / i / Solution

{c}
{title2=$C_{trtr}=-2M/r^3$}

With the curvature convention
$$
R^\alpha{}_{\beta\gamma\delta}
=\partial_\gamma\Gamma^\alpha_{\beta\delta}
-\partial_\delta\Gamma^\alpha_{\beta\gamma}+\cdots,
$$
the vacuum Schwarzschild metric satisfies
$$
C_{trtr}=R_{trtr}=-\frac{2M}{r^3}.
$$
The opposite Riemann-sign convention reverses this sign.


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 Incoming links: Radial Weyl curvature of Schwarzschild spacetime