Knowra Penrose diagram Penrose diagram A spacetime diagram that uses conformal compactification to place infinite distances and times within a finite figure while preserving light-cone structure.
Conformal compactification : A transformation that maps an unbounded space or spacetime into a bounded region while preserving angles or, in spacetime, light cones. This transformation brings infinity onto the diagram’s finite boundary.
Conformal factor : A position-dependent scale factor that relates one metric to another conformally equivalent metric. It rescales the spacetime metric so distant regions fit within finite coordinates.
Schwarzschild spacetime : The vacuum solution of Einstein’s field equations describing the exterior gravitational field of a spherical, nonrotating mass. Its maximally extended diagram displays a black hole, a white hole, and two asymptotic regions.
Spacetime diagram : A graphical representation of events and worldlines in space and time. Penrose diagrams are a specialized spacetime diagram designed to include infinity.
Event horizon : A boundary beyond which events cannot send signals to a distant observer. Its position separates regions that can communicate with infinity from those that cannot.
Minkowski spacetime : The flat spacetime of special relativity, with three spatial dimensions and one time dimension. Its causal structure provides the simplest setting for interpreting a Penrose diagram.
Penrose coordinates : Compact coordinates used to represent an unbounded spacetime within a finite range. They provide the bounded axes on which the diagram is drawn.
Kruskal–Szekeres coordinates : A coordinate system that extends the Schwarzschild solution smoothly across its event horizons. These coordinates expose the full region represented in the standard Schwarzschild Penrose diagram.
Minkowski diagram : A spacetime plot used in special relativity to show inertial frames, events, and light signals. Unlike a compactified Penrose diagram, it usually leaves infinity outside the plotted region.
Black hole : A region of spacetime whose gravity prevents anything, including light, from escaping beyond its event horizon. Penrose diagrams show the black hole’s horizon and interior within the global spacetime.
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