The <curvature 2-forms> show that orthonormal curvature components grow as $m/r^3$. The <geodesic deviation> equation converts them into the relative acceleration of nearby parts of an observer. As $r\to0$, the <Schwarzschild tidal force> stretches radial separations and compresses transverse separations with unbounded magnitude. An extended body therefore undergoes destructive tidal deformation before reaching the <Schwarzschild singularity>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 309 / 4 / e / Solution

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{wiki=Schwarzschild_metric#Singularity}

The Schwarzschild singularity is the spacelike curvature singularity at $r=0$. Curvature invariants and orthonormal tidal components diverge there.


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 Incoming links: Schwarzschild singularity