Penrose diagrams

Definition of a Penrose diagram

A Penrose diagram is a kind of spacetime diagram arranged to make clear the complete causal structure of any given geometry. They are an indispensible map for navigating inside a black hole.

In a Penrose diagram: Light rays move at 45o from the upward vertical; Points at infinity (at infinite distance, or in the infinite past or future) are contained in the diagram.

Penrose diagram of a Schwarzschild black hole

Penrose diagram of the complete Schwarzschild geometry

Penrose diagram of a Reissner-Nordström black hole

The Penrose diagram helps to make sense of the strange experience on your journey into a Reissner-Nordström black hole.

This animated gif (90K) version of the Penrose diagram illustrates how an infaller sees infinitely bright, infinitely blueshifted bursts of light:

On passing inward through the inner horizon, the infaller sees the infinite past of the Universe reflected in the gravitationally repulsive singularity; On passing back outward through the inner horizon, the infaller sees the infinite future of the Universe; On passing outward through the outer horizon of the white hole, the infaller sees the infinite past of the New Universe.

I've given the various regions and horizons of the Reissner-Nordström spacetime names. General relativists do not commonly name all the pieces this way, and they might not agree with my naming choices.

Penrose diagram of an extremal Reissner-Nordström black hole

Penrose diagram of a Kerr black hole

The Penrose diagram of the Kerr geometry for a rotating black hole looks like the Penrose diagram of the Reissner-Nordström geometry for a charged black hole, except that it is possible to pass through the disk bounded by the ring singularity of the rotating black hole to an antiverse.