Kruskal–Szekeres coordinates

E11652

coordinate system maximal analytic extension spacetime coordinate chart

Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

AI illustration

All labels observed (6)

Label	Occurrences
Kruskal–Szekeres coordinates canonical	7
Kruskal–Szekeres extension of the Schwarzschild solution	1
Region I of Kruskal–Szekeres diagram	1
Region III of Kruskal–Szekeres diagram	1
Szekeres–Kruskal coordinates in general relativity	1
maximally extended Kruskal–Szekeres spacetime	1

How this entity was disambiguated

This entity first appeared as the object of triple T65783 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Kruskal–Szekeres coordinates
Context triple: [Schwarzschild black hole, alternativeCoordinates, Kruskal–Szekeres coordinates]

A. Eddington–Finkelstein coordinates
Eddington–Finkelstein coordinates are a coordinate system in general relativity that smoothly covers a black hole’s event horizon, avoiding the coordinate singularity present in standard Schwarzschild coordinates.
B. Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
C. Oppenheimer–Snyder model
The Oppenheimer–Snyder model is a pioneering theoretical description of gravitational collapse in general relativity, providing one of the first rigorous treatments of how a massive star can form a black hole.
D. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
E. The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Kruskal–Szekeres coordinates
Target entity description: Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.

A. Eddington–Finkelstein coordinates
Eddington–Finkelstein coordinates are a coordinate system in general relativity that smoothly covers a black hole’s event horizon, avoiding the coordinate singularity present in standard Schwarzschild coordinates.
B. Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
C. Oppenheimer–Snyder model
The Oppenheimer–Snyder model is a pioneering theoretical description of gravitational collapse in general relativity, providing one of the first rigorous treatments of how a massive star can form a black hole.
D. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
E. The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	coordinate system ⓘ maximal analytic extension ⓘ spacetime coordinate chart ⓘ
appearsIn	literature on black hole physics ⓘ textbooks on general relativity ⓘ
appliesTo	Schwarzschild metric ⓘ linked to: Schwarzschild black hole spherically symmetric vacuum solution ⓘ
assumes	non-rotating black hole ⓘ uncharged black hole ⓘ
basedOn	Schwarzschild coordinates ⓘ
coordinateType	global coordinates ⓘ null-like coordinates ⓘ regular coordinates at the event horizon ⓘ
describes	regions inside the Schwarzschild event horizon ⓘ regions outside the Schwarzschild event horizon ⓘ second asymptotically flat region of Schwarzschild spacetime ⓘ white hole region of Schwarzschild spacetime ⓘ
domain	regions I, II, III, and IV of Schwarzschild spacetime ⓘ
enables	analysis of geodesic completeness of Schwarzschild spacetime ⓘ study of causal connections between different regions ⓘ visualization of black hole and white hole regions ⓘ
feature	light cones appear at 45 degrees in Kruskal diagrams ⓘ metric is finite at the event horizon ⓘ timelike and spacelike character of coordinates changes across regions ⓘ
field	general relativity ⓘ
introducedBy	George Szekeres ⓘ Martin David Kruskal ⓘ
massParameter	M ⓘ
mathematicalNature	analytic coordinate transformation ⓘ conformal to part of Minkowski-like plane ⓘ
namedAfter	George Szekeres ⓘ Martin David Kruskal ⓘ
preserves	curvature singularity at r = 0 ⓘ
relatedConcept	Schwarzschild radius ⓘ causal structure ⓘ curvature singularity ⓘ event horizon ⓘ geodesic completeness ⓘ
relatedTo	Eddington–Finkelstein coordinates ⓘ Penrose–Carter diagrams ⓘ maximal analytic extension of black hole spacetimes ⓘ
removes	coordinate singularity at r = 2M ⓘ
usedFor	describing Schwarzschild spacetime ⓘ describing the full maximally extended Schwarzschild black hole ⓘ drawing Kruskal diagrams ⓘ extending Schwarzschild solution across the event horizon ⓘ removing coordinate singularity at the Schwarzschild radius ⓘ studying causal structure of Schwarzschild spacetime ⓘ
yearProposed	1960 ⓘ

How these facts were elicited