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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 region called "null infinity", or to singularities where light rays must end. Thus, Penrose diagrams are also useful in the study of asymptotic properties of ...
The Penrose diagram for Minkowski spacetime. Radial position is on the horizontal axis and time is on the vertical axis. Null infinity is the diagonal boundary of the diagram, designated with script 'I'. The metric for a flat Minkowski spacetime in spherical coordinates is = + +.
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A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches.
In these coordinates, the horizon is the black hole horizon (nothing can come out). The diagram for u-r coordinates is the same diagram turned upside down and with u and v interchanged on the diagram. In that case the horizon is the white hole horizon, which matter and light can come out of, but nothing can go in.
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Roger Penrose's solution of the illumination problem using elliptical arcs (blue) and straight line segments (green), with 3 positions of the single light source (red spot). The purple crosses are the foci of the larger arcs.
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