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.

AI illustration

How this image was made

AI-generated illustration of Painlevé–Gullstrand coordinates

This AI-generated illustration was produced by black-forest-labs/FLUX.2-dev (1024x1024) from a prompt written by openai/gpt-oss-120b from the entity's label + description.

Prompt

Generate an image of Painlevé–Gullstrand coordinates (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)

How this entity was disambiguated

Statements (48)

Predicate Object
instanceOf black hole coordinate system ⓘ
coordinate system ⓘ
spacetime coordinate chart ⓘ
appliesTo Schwarzschild black hole ⓘ
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 radial coordinate ⓘ
hasTimeCoordinate Painlevé–Gullstrand time ⓘ
hasVariant ingoing Painlevé–Gullstrand coordinates ⓘ
outgoing Painlevé–Gullstrand coordinates ⓘ
inspired use in analogue gravity for flowing media ⓘ
isAlternativeTo Boyer–Lindquist-type horizon-avoiding coordinates ⓘ
isRegularAt 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 ⓘ
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

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Eddington–Finkelstein coordinates → relatedTo → Painlevé–Gullstrand coordinates ⓘ
Painlevé–Gullstrand coordinates → relatedTo → Lemaître coordinates ⓘ
linked to: Painlevé–Gullstrand coordinates
Painlevé–Gullstrand coordinates → hasTimeCoordinate → Painlevé–Gullstrand time ⓘ
linked to: Painlevé–Gullstrand coordinates
Painlevé–Gullstrand coordinates → hasVariant → ingoing Painlevé–Gullstrand coordinates ⓘ
linked to: Painlevé–Gullstrand coordinates
Painlevé–Gullstrand coordinates → hasVariant → outgoing Painlevé–Gullstrand coordinates ⓘ
linked to: Painlevé–Gullstrand coordinates