Penrose Diagram - Basic Properties

Basic Properties

While Penrose diagrams share the same basic coordinate vector system of other space-time diagrams for local asymptotically flat spacetime, it introduces a system of representing distant spacetime by shrinking or "crunching" distances that are further away. Straight lines of constant time and space coordinates therefore become hyperbolas, which appear to converge at points in the corners of the diagram. These points represent "conformal infinity" for space and time.

Penrose diagrams are more properly (but less frequently) called Penrose-Carter diagrams (or Carter-Penrose diagrams), acknowledging both Brandon Carter and Roger Penrose, who were the first researchers to employ them. They are also called conformal diagrams, or simply spacetime diagrams.

Two lines drawn at 45° angles should intersect in the diagram only if the corresponding two light rays intersect in the actual spacetime. So, a Penrose diagram can be used as a concise illustration of spacetime regions that are accessible to observation. The diagonal boundary lines of a Penrose diagram correspond to the "infinity" or to singularities where light rays must end. Thus, Penrose diagrams are also useful in the study of asymptotic properties of spacetimes and singularities. An infinite static Minkowski universe, coordinates is related to Penrose coordinates by:

The corners of the Penrose diamond, which represent the spacelike and timelike conformal infinities, are from the origin.