Conformal Diagrams

A conformal diagram records causal incidence in a finite picture: which null curves meet, which boundaries they reach, and which regions belong to the spacetime. It does not preserve metric lengths, angles away from the drawn null directions, areas, or affine parameters. The records in this directory therefore pair every diagram with a domain statement, time orientation, boundary key, and link to its full construction.

Helpful background. Causality and Global Structure supplies causal relations, horizons, conformal boundaries, and the distinction between local cones and global causal claims.

Available diagrams

Record	Use it to identify	Critical scope
Minkowski Conformal Diagram	The regular radial center, $\mathscr I^\pm$, $i^\pm$, $i^0$, and the endpoints of representative null, timelike, and spacelike curves	Four-dimensional spherical radial quotient; a triangle rather than the full $1+1$ diamond
Maximally Extended Schwarzschild Diagram	The four Kruskal regions, horizon branches, bifurcation two-sphere, singular boundaries, and two asymptotic ends	Eternal maximal analytic vacuum extension, not a formed black hole
Black Hole Formed by Collapse	A regular past center, timelike matter surface, globally defined event horizon, one asymptotic end, and future singularity	Original marginally bound Oppenheimer–Snyder branch: the surface emanates from $i^-$ and its radius tends to infinity to the past; not a finite-radius initial-data development or generic collapse
Reissner–Nordström Conformal Diagrams	How two simple roots, one double root, or no root produce subextremal, extremal, and superextremal causal graphs	Exact analytic electrovac backgrounds; no claim about stability, formation, or censorship
de Sitter and Anti-de Sitter Conformal Diagrams	Spacelike de Sitter infinity and observer horizons versus timelike anti-de Sitter infinity and finite global light travel	Exact global $d\ge3$ backgrounds; anti-de Sitter time is unwrapped and no boundary condition or Poincaré wedge is built into the global diagram
Evaporating Black-Hole Diagram Families	The boundary between fixed-background radiation, controlled backreaction, and an explicitly assumed future completion	Representative four-dimensional spherical sketches, not a unique endpoint prediction or an information-flow diagram

The sequence is deliberate. Minkowski fixes the compactification and endpoint vocabulary; eternal Schwarzschild adds horizons, two exteriors, and black- and white-hole regions; collapse shows which past regions disappear in the selected one-ended matter model; Reissner–Nordström isolates how charge changes root multiplicity, singularity character, and analytic repetition; de Sitter and anti-de Sitter show how the sign of $\Lambda$ changes the causal character of infinity and the evolution problem; evaporation then shows why a controlled partial history does not select its own global future. Use the Schwarzschild coordinate record for metric components and chart overlaps, The Maximal Schwarzschild Extension for the analytic vacuum derivation, Reissner–Nordström Horizons and Extensions for the charged construction, the de Sitter and anti-de Sitter chart record for global, static, planar, and Poincaré coordinate coverage, and Hawking Flux, Backreaction, and Evaporation Dynamics for the physical approximation hierarchy.

What the picture preserves

In the spherically symmetric examples collected here, the drawing represents the two-dimensional orbit space obtained after suppressing the symmetry orbits. Radial null directions are drawn at $45^\circ$, and future points upward. Each ordinary interior point represents an $S^{d-2}$ symmetry orbit—a two-sphere in four spacetime dimensions—rather than a single event of the full spacetime.

Before using any diagram, check:

1. Physical domain. Is the picture maximal, exterior-only, or selected by collapse initial data?
2. Boundary character. Is each edge null, spacelike, timelike, regular, singular, or an ideal conformal boundary?
3. Orientation. Which way is future, and which components are $\mathscr I^+$ and $\mathscr I^-$?
4. Suppressed geometry. What symmetry or quotient turns the spacetime into the displayed two-dimensional picture?
5. Scope. Which conclusions follow only from causal order, and which require the original metric, curvature, or affine parametrization?

The construction procedure and its independent domain checks are developed in Constructing Penrose Diagrams. For definitions of null and timelike infinity, see Future and Past Null Infinity and Timelike, Spacelike, and Spatial Infinity.