bcrowell said:What I find hard about the subject is that it seems to have undergone a process of gradual generalization, but Penrose's is the only attempt I've seen to go back and give a synoptic view, and Penrose's treatment is nonmathematical. I haven't seen a clear, mathematically detailed description of what the fundamental principles are that apply in general. Everybody just presents certain special cases.
A Penrose diagram is a graphical representation of the spacetime structure of a particular region in a curved spacetime. It was developed by physicist Roger Penrose in order to visualize the causal relationships between different events in a spacetime.
To construct a Penrose diagram, one first chooses a coordinate system for the spacetime and then performs a conformal transformation on the coordinates. This transformation maps the entire spacetime onto a finite region, with the boundary of the region representing infinity. The resulting diagram is a two-dimensional representation of the four-dimensional spacetime.
Penrose diagrams are useful for understanding the global structure of a spacetime, particularly in cases where the spacetime is highly curved or contains black holes. They also allow for easier visualization of the paths of light rays and other particles through the spacetime.
Penrose diagrams are only applicable to spacetimes that are stationary, meaning that they do not change over time. They also do not accurately represent the distances between different points in the spacetime, as the conformal transformation distorts the distances.
Yes, there are several books and articles that provide more in-depth explanations and applications of Penrose diagrams. Some recommended references include "The Road to Reality" by Roger Penrose, "The Geometry of Spacetime" by James J. Callahan, and "Black Holes: The Membrane Paradigm" by Kip S. Thorne.