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As long as I'm posting diagrams, here is the Kruskal diagram for the Schwarzschild spacetime. Hyperbolas (blue) are constant r, and straight lines (red) are constant t. The 45 degree lines (purple) crossing the origin are the horizon, and the bold hyperbola (black) is the singularity.
Schwarzschild's coordinates cover the gray patch, Eddington-Finkelstein coordinates cover the orange patch, and Kruskal-Szekeres coordinates the entire (orange + green) shaded region.
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