Penrose Diagram
The maximally extended Schwarzschild spacetime drawn as a finite square. Infinity gets compressed to the diagonal edges. Light cones are always at 45°. Four regions appear: our universe, a parallel universe we can't reach, a black hole interior, and a white hole interior we can't enter. Roger Penrose, 1965 — turns the unwieldy infinite spacetime into a picture you can fit in your head.
how to read the diagram
A Penrose diagram uses a conformal transformation to map infinite spacetime regions onto finite areas, while preserving the causal structure. Light rays always travel at 45°. Distances are distorted near infinity, but what could ever causally influence what is preserved exactly.
The maximally extended Schwarzschild diagram has four labeled regions:
Region I (right) — our universe. Time runs upward; space runs outward. Distant observers live here.
Region II (top) — the black hole interior. To get here, you cross the event horizon (the 45° line marked H⁺). Inside, the radial direction becomes timelike: you can no longer choose to move outward, only toward the singularity at the top (the wavy line).
Region III (left) — a parallel universe. Causally disconnected from us; we'd need to travel faster than light to reach it.
Region IV (bottom) — the white hole interior. The time-reverse of Region II. Matter comes out of it but nothing can fall in. Probably not physical — eternal Schwarzschild has it, but real astrophysical black holes (formed by collapse) don't.
Drag the observer. Once you cross the horizon (H⁺), the singularity is in your future — there's no possible 45° (or less steep) line from you that avoids it. Falling in is geometrically inevitable. This is the precise sense in which a black hole's interior is a place from which nothing returns: it isn't a place at all, it's a time.