Curvature invariants and the electromagnetic invariant diverge at $r=0$, so it is a genuine <curvature singularity>, not a coordinate singularity. The causal structures are the higher-dimensional analogues of the familiar four-dimensional diagrams:

* for $r_-=0$, there is one nondegenerate horizon and a spacelike singularity, giving the Schwarzschild Penrose diagram;
* for $0<r_-<r_+$, the outer event horizon and inner <Cauchy horizon> enclose a region ending at a timelike singularity, with the maximally extended Reissner-Nordström chain of blocks;
* for $r_-=r_+$, the horizon is degenerate with $\kappa=0$, the singularity remains timelike, and the extremal throat has infinite spatial length.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 311 / 2 / d / Solution

A curvature singularity is an incomplete spacetime boundary approached by curves along which a scalar curvature invariant or a component of the <Riemann curvature tensor> in a parallel-propagated frame becomes unbounded. Such divergence cannot be removed by changing coordinates.

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