Painlevé–Gullstrand coordinates
E65088
Painlevé–Gullstrand coordinates are a coordinate system for the Schwarzschild black hole that is regular at the event horizon and represents spacetime as seen by freely falling observers.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Lemaître coordinates | 1 |
| Painlevé–Gullstrand coordinates canonical | 1 |
| Painlevé–Gullstrand time | 1 |
| ingoing Painlevé–Gullstrand coordinates | 1 |
| outgoing Painlevé–Gullstrand coordinates | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T518676 — 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.
Target entity: Painlevé–Gullstrand coordinates Context triple: [Eddington–Finkelstein coordinates, relatedTo, Painlevé–Gullstrand coordinates]
-
A.
Kruskal–Szekeres coordinates
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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B.
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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C.
Schwarzschild coordinates
Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.
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D.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
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E.
Reissner–Nordström metric
The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Painlevé–Gullstrand coordinates Target entity description: Painlevé–Gullstrand coordinates are a coordinate system for the Schwarzschild black hole that is regular at the event horizon and represents spacetime as seen by freely falling observers.
-
A.
Kruskal–Szekeres coordinates
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.
-
B.
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.
-
C.
Schwarzschild coordinates
Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.
-
D.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
-
E.
Reissner–Nordström metric
The Reissner–Nordström metric is an exact solution in general relativity describing the spacetime geometry outside a static, spherically symmetric, electrically charged black hole.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
black hole coordinate system
ⓘ
coordinate system ⓘ spacetime coordinate chart ⓘ |
| appliesTo |
Schwarzschild black hole
ⓘ
Schwarzschild black hole ⓘ
surface form:
Schwarzschild spacetime
|
| belongsTo |
black hole physics
ⓘ
differential geometry ⓘ mathematical physics ⓘ |
| coordinateType |
ADM-like slicing with flat spatial metric
ⓘ
non-orthogonal coordinates ⓘ |
| describes |
ingoing geodesic congruence
ⓘ
radial infall of test particles ⓘ |
| describesPerspectiveOf | freely falling observers ⓘ |
| expresses | Schwarzschild solution in free-fall frame ⓘ |
| feature |
light cones tilt smoothly across horizon
ⓘ
no coordinate singularity at Schwarzschild radius ⓘ time coordinate coincides with proper time of specific infalling observers ⓘ |
| hasInterpretation | space flowing into the black hole ⓘ |
| hasProperty |
adapted to radial free fall from rest at infinity
ⓘ
horizon-penetrating ⓘ non-singular at event horizon ⓘ spatially flat slices ⓘ stationary but not static ⓘ synchronous time coordinate for infalling observers ⓘ |
| hasSpatialCoordinates |
Schwarzschild angular coordinates
ⓘ
Schwarzschild coordinates ⓘ
surface form:
Schwarzschild radial coordinate
|
| hasTimeCoordinate |
Painlevé–Gullstrand coordinates
self-linksurface differs
ⓘ
surface form:
Painlevé–Gullstrand time
|
| hasVariant |
Painlevé–Gullstrand coordinates
self-linksurface differs
ⓘ
surface form:
ingoing Painlevé–Gullstrand coordinates
Painlevé–Gullstrand coordinates self-linksurface differs ⓘ
surface form:
outgoing Painlevé–Gullstrand coordinates
|
| inspired | use in analogue gravity for flowing media ⓘ |
| isAlternativeTo | Boyer–Lindquist-type horizon-avoiding coordinates ⓘ |
| isRegularAt |
Schwarzschild radius
ⓘ
surface form:
Schwarzschild event horizon
|
| metricForm |
contains off-diagonal time–radial term
ⓘ
spatial 3-metric is Euclidean in constant-time slices ⓘ |
| namedAfter |
Allvar Gullstrand
ⓘ
Paul Painlevé ⓘ |
| relatedTo |
Eddington–Finkelstein coordinates
ⓘ
Kruskal–Szekeres coordinates ⓘ Painlevé–Gullstrand coordinates self-linksurface differs ⓘ
surface form:
Lemaître coordinates
Schwarzschild coordinates ⓘ |
| usedFor |
acoustic black hole analogues
ⓘ
analogue gravity models ⓘ numerical relativity toy models ⓘ studying black hole horizons ⓘ visualizing infalling frames ⓘ |
| usedIn |
general relativity
ⓘ
pedagogical treatments of black holes ⓘ |
| yearProposed | 1921 ⓘ |
How these facts were elicited
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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.
Subject: Painlevé–Gullstrand coordinates Description of subject: Painlevé–Gullstrand coordinates are a coordinate system for the Schwarzschild black hole that is regular at the event horizon and represents spacetime as seen by freely falling observers.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.