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)

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