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 timelike 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? How to do I actually combine it with the (rather abstract) definition of a naked singularity?
Many thanks!
Try R. M. Wald's General Relativity. He's got some pretty good descriptions of singularities (Chapter 9). As a rough idea, I think you could try defining some singular metric, e.g., in, Cartesian coordinates: $ds^2 = (1/r^2) (-dt^2 + dx^2 + dy^2 + dz^2)$, do calculations involving a curvature scalar such as $R^{abcd}R_{abcd}$ to show it becomes singular when $r := \sqrt{x^2 + y^2 + z^2} \rightarrow 0$, and then consider a radial null geodesic "passing through" $0$ in these coordinates. You'll need to show there exists such a geodesic which is inextendible past $0$, but has a finite range of affine parameter in that direction.