Radial Weyl curvature of Schwarzschild spacetime ($C_{trtr}=-2M/r^3$)

With the curvature conventionthe vacuum Schwarzschild metric satisfiesThe opposite Riemann-sign convention reverses this sign.

The orthonormal-frame components of Schwarzschild curvature scale as $M/r^3$. The geodesic deviation equation therefore gives radial stretching and transverse compression whose magnitude diverges as $r\to 0$.

Weyl curvature produces relative acceleration between neighbouring freely falling trajectories and therefore tidal deformation. A freely falling frame removes gravity at one event, as required by the equivalence principle, but cannot remove curvature over an extended region.