Painlevé–Gullstrand coordinates

E65088

black hole coordinate system coordinate system spacetime coordinate chart

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.

Jump to: Surface forms Statements Referenced by

Observed surface forms (4)

Surface form	Occurrences
Lemaître coordinates	1
Painlevé–Gullstrand time	1
ingoing Painlevé–Gullstrand coordinates	1
outgoing Painlevé–Gullstrand coordinates	1

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 ⓘ

Referenced by (5)

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

Painlevé–Gullstrand coordinates → hasTimeCoordinate → Painlevé–Gullstrand coordinates self-linksurface differs ⓘ

this entity surface form: Painlevé–Gullstrand time

Painlevé–Gullstrand coordinates → hasVariant → Painlevé–Gullstrand coordinates self-linksurface differs ⓘ

this entity surface form: ingoing Painlevé–Gullstrand coordinates

Painlevé–Gullstrand coordinates → hasVariant → Painlevé–Gullstrand coordinates self-linksurface differs ⓘ

this entity surface form: outgoing Painlevé–Gullstrand coordinates

Eddington–Finkelstein coordinates → relatedTo → Painlevé–Gullstrand coordinates ⓘ

Painlevé–Gullstrand coordinates → relatedTo → Painlevé–Gullstrand coordinates self-linksurface differs ⓘ

this entity surface form: Lemaître coordinates