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Black hole topology
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In relativistic astrophysics, the spacetime curvature near any massive object can be understood as a "gravity well", see image. For most massive objects the well has a closed dip, forming a continuous surface. For a black hole, the intense gravitation causes this dip to become "punctured". Singularity Near a black hole, we can draw geodesics as in the image above, although at the singularity, all laws of physics break down completely (including general relativity) due to an infinity arising in the line element of the solution to the Einstein field equations, and it's not obvious what the spacetime geometry is like. The region of spacetime within the Schwarzschild radius of a black hole is so highly curved that even a beam of light could not escape the region; the escape speed is greater than light within that region. See Also
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