Schwarzschild coordinates
E41074
Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Schwarzschild coordinates canonical | 8 |
| Schwarzschild radial coordinate | 1 |
| Schwarzschild-like coordinates | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T311431 — 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: Schwarzschild coordinates Context triple: [Schwarzschild radius, coordinateSingularityAt, Schwarzschild coordinates]
-
A.
Eddington–Finkelstein coordinates
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.
-
B.
Kruskal–Szekeres coordinates
Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.
-
C.
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.
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D.
Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
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E.
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.
- 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: Schwarzschild coordinates Target entity description: Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.
-
A.
Eddington–Finkelstein coordinates
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.
-
B.
Kruskal–Szekeres coordinates
Kruskal–Szekeres coordinates are a maximal extension coordinate system used in general relativity to smoothly describe the entire spacetime of a Schwarzschild black hole, including regions across the event horizon.
-
C.
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.
-
D.
Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
-
E.
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
coordinate system
ⓘ
general relativity concept ⓘ spherical coordinate system ⓘ |
| associatedWith |
Schwarzschild radius
ⓘ
Schwarzschild solution ⓘ
linked to:
Schwarzschild black hole
event horizon of a Schwarzschild black hole ⓘ |
| assumes |
non-rotating central mass
ⓘ
spherical symmetry ⓘ static spacetime ⓘ |
| contrastsWith | Kerr coordinates for rotating black holes ⓘ |
| describes |
Schwarzschild metric
ⓘ
linked to:
Schwarzschild black hole
exterior region of a static black hole ⓘ spacetime outside a spherically symmetric non-rotating mass ⓘ vacuum solution of Einstein field equations with spherical symmetry ⓘ |
| domainOfAzimuthalAngle | 0 ≤ φ < 2π ⓘ |
| domainOfPolarAngle | 0 ≤ θ ≤ π ⓘ |
| domainOfRadialCoordinate | 0 < r < ∞ ⓘ |
| domainOfTimeCoordinate | -∞ < t < ∞ ⓘ |
| hasCoordinate |
r
ⓘ
t ⓘ θ ⓘ φ ⓘ |
| hasCoordinateSingularityAt | Schwarzschild radius ⓘ |
| hasCoordinateType |
azimuthal angle φ
ⓘ
polar angle θ ⓘ radial coordinate r ⓘ time coordinate t ⓘ |
| hasLimitation |
breaks down at the event horizon
ⓘ
not regular across r = 2GM/c^2 ⓘ |
| hasLineElementForm | ds^2 = -(1-2GM/r)c^2 dt^2 + (1-2GM/r)^{-1} dr^2 + r^2(dθ^2 + sin^2θ dφ^2) ⓘ |
| hasMetricSignature | (-,+,+,+) ⓘ |
| hasPhysicalSingularityAt | r = 0 ⓘ |
| introducedInContextOf | exact solutions of Einstein field equations ⓘ |
| mathematicallyDefinedOn |
Schwarzschild manifold
ⓘ
linked to:
Schwarzschild black hole
|
| namedAfter | Karl Schwarzschild ⓘ |
| relatedTo |
Eddington–Finkelstein coordinates
ⓘ
Kruskal–Szekeres coordinates ⓘ isotropic coordinates ⓘ |
| usedFor |
calculating gravitational redshift
ⓘ
calculating light deflection by gravity ⓘ calculating perihelion precession ⓘ studying radial infall into a black hole ⓘ studying test particle orbits ⓘ |
| usedIn | general relativity ⓘ |
| usedToDescribe |
gravitational field outside a non-rotating black hole
ⓘ
gravitational field outside a planet ⓘ gravitational field outside a star ⓘ |
| usesUnits | geometrized units in many treatments ⓘ |
| validFor | r greater than Schwarzschild radius ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Schwarzschild coordinates Description of subject: Schwarzschild coordinates are a spherical coordinate system used in general relativity to describe the spacetime geometry outside a spherically symmetric, non-rotating mass, such as a static black hole.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Schwarzschild coordinates
linked to: Schwarzschild coordinates
subject linked to:
Schwarzschild
subject linked to:
Karl