I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually show it).


Based on what (little) is written in Choquet-Bruhat's, a naked singularity is the one for which we can extend the outgoing time-like geodesics to infinity. Now, I was wondering, assuming I had a *given solution*, how would I "test" the nakedness of the singularity? A natural thing to do would be to write the solution in some null coordinates, but what then? (the idea of writing it in null coordinates came from this qustion [Christodoulou's paper on naked singularities in inhomogeneous dust collapse](https://mathoverflow.net/questions/37812/christodoulous-paper-on-naked-singularities-in-inhomogeneous-dust-collapse))



naked singularity and null coordinates
The formal definition of a naked singularity can be found in standard GR books (Wald, Hawking & Ellis, probably others). However, here's a slightly crude, rule of thumb way of checking whether your spacetime has a singularity and whether it is naked. There is a singularity if an affinely parametrized causal curve (past or future directed) reaches an infinite value for some curvature scalar in finite time (say Kretschmann scalar). If there are two curves, say A and B, such that A is future oriented, B is past oriented, B is in the future (domain of influence) of A, and both A and B end in a singularity, then the singularity is naked.


One can play around with other ways of checking for a singularity besides diverging curvature scalars. One can also require that instead of a single geodesic (or a single pair) there are geodesic congruences that all behave in the same way. These all correspond to more sophisticated ways of identifying singularities.


Specifically about null coordinates, they can help if your the coordinate curves parametrized by the null coordinate reach the singularity in the way described above.


