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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All labels observed (3)

Label	Occurrences
Eddington–Finkelstein coordinates canonical	7
ingoing Eddington–Finkelstein coordinates	1
outgoing Eddington–Finkelstein coordinates	1

How this entity was disambiguated

This entity first appeared as the object of triple T65782 — 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.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Eddington–Finkelstein coordinates
Context triple: [Schwarzschild black hole, alternativeCoordinates, Eddington–Finkelstein coordinates]

A. Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
B. Oppenheimer–Snyder model
The Oppenheimer–Snyder model is a pioneering theoretical description of gravitational collapse in general relativity, providing one of the first rigorous treatments of how a massive star can form a black hole.
C. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
D. The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
E. Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Eddington–Finkelstein coordinates
Target entity description: 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.

A. Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
B. Oppenheimer–Snyder model
The Oppenheimer–Snyder model is a pioneering theoretical description of gravitational collapse in general relativity, providing one of the first rigorous treatments of how a massive star can form a black hole.
C. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
D. The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
E. Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
F. None of above. chosen

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 ⓘ

How these facts were elicited

Referenced by (9)

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

Schwarzschild black hole → alternativeCoordinates → 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

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

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

Schwarzschild coordinates → relatedTo → Eddington–Finkelstein coordinates ⓘ

Arthur Stanley Eddington → knownFor → Eddington–Finkelstein coordinates ⓘ

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

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

All labels observed (3)

How this entity was disambiguated Show

Statements (51)

How these facts were elicited Show

Referenced by (9)

How this entity was disambiguated

How these facts were elicited