Kruskal–Szekeres coordinates
E11652
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.
All labels observed (6)
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]
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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.
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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.
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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.
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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.
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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.
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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 black hole
ⓘ
surface form:
Schwarzschild metric
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
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Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Kruskal–Szekeres coordinates Description of subject: 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.
Referenced by (12)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
maximally extended Kruskal–Szekeres spacetime
this entity surface form:
Region I of Kruskal–Szekeres diagram
this entity surface form:
Region III of Kruskal–Szekeres diagram
this entity surface form:
Szekeres–Kruskal coordinates in general relativity
this entity surface form:
Kruskal–Szekeres extension of the Schwarzschild solution