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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?

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Could you give a reference for this: the metric defines the light cone, so in a sense it's already extended "beyond the light cone". Maybe you're referring to maximal analytic extension? – twistor59 May 10 '13 at 12:41
@twistor, yes I did look at that thread but as I mentioned in the question, it only concerns with re-writing the Schwarzschild metric so that no coordinate singularities appear. I thought more in this direction: if the construction was carried out on a particular patch (just the past light cone), how could I extend it beyond the past light cone, i.e. to see whether I could potentially hit the BH horizon or, in case there is no horizon, one hits a naked singularity – ConciseAndClear May 10 '13 at 12:49
can anyone help please? – ConciseAndClear May 10 '13 at 13:39
It's very hard to imagine your example of a past light cone being generated other than by taking a spacetime and saying I'm just going to look at the manifold inside the past light cone and ignore everything else. i.e. your past light cone has been defined by a restriction operation, in which case there's an obvious extension! I don't know of any algorithm for generating maximal extensions - if you gave me Schwarzschild, I'd never have "guessed" the Kruskal extension - it's a rather ingenious construction. – twistor59 May 10 '13 at 19:05

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