Eddington–Finkelstein coordinates

E10764

Eddington–Finkelstein coordinate system coordinate system in general relativity spacetime coordinate chart

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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Observed surface forms (2)

Surface form	Occurrences
ingoing Eddington–Finkelstein coordinates	1
outgoing Eddington–Finkelstein coordinates	1

Statements (51)

Predicate	Object
instanceOf	Eddington–Finkelstein coordinate system ⓘ Eddington–Finkelstein coordinate system ⓘ coordinate system in general relativity ⓘ spacetime coordinate chart ⓘ
appliesTo	non-rotating uncharged black holes ⓘ
category	Lorentzian geometry ⓘ black hole coordinates ⓘ
coordinateSymbols	(u, r, θ, φ) ⓘ (v, r, θ, φ) ⓘ
coordinateType	null coordinate system ⓘ spherical symmetry adapted coordinates ⓘ
definedOn	Schwarzschild black hole ⓘ surface form: Schwarzschild spacetime
dimension	4 ⓘ
eventHorizonRadiusSymbol	r = 2M ⓘ
generalizationOf	Eddington’s original coordinates for the Schwarzschild solution ⓘ
hasVariant	Eddington–Finkelstein coordinates self-linksurface differs ⓘ surface form: ingoing Eddington–Finkelstein coordinates Eddington–Finkelstein coordinates self-linksurface differs ⓘ surface form: outgoing Eddington–Finkelstein coordinates
helpsExplain	infall of light and matter across the event horizon ⓘ one-way nature of classical black hole event horizons ⓘ
historicalDevelopment	Eddington introduced a form of the coordinates in the 1920s ⓘ Finkelstein clarified their causal interpretation in 1958 ⓘ
introducedFor	clarifying the nature of the Schwarzschild radius ⓘ showing that the Schwarzschild radius is not a physical singularity ⓘ
mainCoordinateSymbol	u ⓘ v ⓘ
metricSignature	(-,+,+,+) ⓘ
namedAfter	Arthur Stanley Eddington ⓘ David Finkelstein ⓘ
property	adapted to radial null geodesics ⓘ metric contains off-diagonal term in dv dr or du dr ⓘ non-static metric form ⓘ regular at the event horizon ⓘ remove the coordinate singularity at r = 2M in Schwarzschild coordinates ⓘ
relatedTo	Kruskal–Szekeres coordinates ⓘ Painlevé–Gullstrand coordinates ⓘ Schwarzschild coordinates ⓘ null coordinates ⓘ
timeCoordinateType	advanced time ⓘ advanced time ⓘ retarded time ⓘ retarded time ⓘ
underlyingTheory	general relativity ⓘ
usedFor	analyzing radial null geodesics ⓘ describing Schwarzschild black holes ⓘ describing spacetime near a black hole event horizon ⓘ extending Schwarzschild solution across the event horizon ⓘ removing coordinate singularities at the event horizon ⓘ studying causal structure of black hole spacetimes ⓘ
usedIn	Penrose diagram constructions for Schwarzschild spacetime ⓘ discussions of gravitational collapse ⓘ textbooks on general relativity ⓘ

Referenced by (9)

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

Schwarzschild black hole → alternativeCoordinates → Eddington–Finkelstein coordinates ⓘ

Reissner–Nordström metric → canBeExtendedBy → Eddington–Finkelstein coordinates ⓘ

Eddington–Finkelstein coordinates → hasVariant → Eddington–Finkelstein coordinates self-linksurface differs ⓘ

this entity surface form: ingoing Eddington–Finkelstein coordinates

Eddington–Finkelstein coordinates → hasVariant → Eddington–Finkelstein coordinates self-linksurface differs ⓘ

this entity surface form: outgoing Eddington–Finkelstein coordinates

Arthur Stanley Eddington → knownFor → Eddington–Finkelstein coordinates ⓘ

Kerr–Schild coordinates → relatedTo → Eddington–Finkelstein coordinates ⓘ

Kruskal–Szekeres coordinates → relatedTo → Eddington–Finkelstein coordinates ⓘ

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

Schwarzschild coordinates → relatedTo → Eddington–Finkelstein coordinates ⓘ