Could anyone explain what "extending the solution" beyond the past light cone means? Say, for example, if I have a metric (no coordinate singularities), how can I extend it to the outside of the past light cone?
Up to know, I only could find the extension argument in the context of Schwarzschild solution, where it seemed to be simply the procedure of removing a coordinate singularity. So what if I don't have a coordinate singularity, how do I show the extension of my solution? What mathematical techniques does "extending the solution" imply?