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I was wondering about the following - in GR texts we always see these penrose diagrams and some line representing the horizon and all these timelike , spacelike curves and all that ... but the picture that I have of GR is just that of a smooth 4 manifold endowed with a metric . Can I view black holes in such a picture? For example, this event horizon is a submanifold and the singularity as some point which cannot be covered by any coordinate patch ? Thanks for any help ..

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# How to view black holes / horizon from a manifold perspective

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