Boyer–Lindquist coordinates
E77120
Boyer–Lindquist coordinates are a spheroidal coordinate system commonly used in general relativity to express the Kerr solution describing the spacetime around a rotating black hole.
All labels observed (5)
How this entity was disambiguated
This entity first appeared as the object of triple T616520 — 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: Boyer–Lindquist coordinates Context triple: [Kerr metric, hasCoordinateSystem, Boyer–Lindquist coordinates]
-
A.
Schwarzschild coordinates
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.
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B.
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.
-
C.
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.
-
D.
Painlevé–Gullstrand coordinates
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.
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E.
Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged 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: Boyer–Lindquist coordinates Target entity description: Boyer–Lindquist coordinates are a spheroidal coordinate system commonly used in general relativity to express the Kerr solution describing the spacetime around a rotating black hole.
-
A.
Schwarzschild coordinates
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.
-
B.
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.
-
C.
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.
-
D.
Painlevé–Gullstrand coordinates
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.
-
E.
Kerr metric
The Kerr metric is the exact general relativity solution describing the spacetime geometry around a rotating, uncharged black hole.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
coordinate system
ⓘ
curvilinear coordinate system ⓘ spheroidal coordinate system ⓘ |
| coordinateSingularityAt |
event horizon of Kerr black hole
ⓘ
Δ = 0 ⓘ |
| definesFunction |
Δ = r^2 - 2Mr + a^2 + Q^2
ⓘ
Σ = r^2 + a^2 cos^2θ ⓘ |
| domainOfDefinition |
0 ≤ θ ≤ π
ⓘ
0 ≤ φ < 2π ⓘ r > 0 ⓘ |
| generalizes | Schwarzschild coordinates ⓘ |
| hasCoordinate |
r
ⓘ
t ⓘ θ ⓘ φ ⓘ |
| hasParameter |
charge Q
ⓘ
mass M ⓘ spin parameter a ⓘ |
| hasProperty |
adapted to axial symmetry
ⓘ
asymptotically spherical at large r ⓘ reduce to Schwarzschild coordinates when a=0 ⓘ time coordinate t is asymptotically Minkowskian ⓘ θ is polar angle from rotation axis ⓘ φ is azimuthal angle around rotation axis ⓘ |
| hasSignature | (-,+,+,+) ⓘ |
| hasSymmetry |
axisymmetry
ⓘ
stationarity ⓘ |
| introducedBy |
Richard W. Lindquist
ⓘ
Robert H. Boyer ⓘ |
| introducedInContext |
Kerr solution
ⓘ
linked to:
Kerr metric
|
| metricComponent |
g_rr = Σ/Δ
ⓘ
g_tt = -(1 - 2Mr/Σ) ⓘ g_tφ = -2Mar sin^2θ / Σ ⓘ g_θθ = Σ ⓘ g_φφ = (r^2 + a^2 + 2Ma^2 r sin^2θ / Σ) sin^2θ ⓘ |
| relatedTo |
Boyer–Lindquist r coordinate
ⓘ
linked to:
Boyer–Lindquist coordinates
Boyer–Lindquist time coordinate ⓘ
linked to:
Boyer–Lindquist coordinates
Eddington–Finkelstein coordinates ⓘ Kerr–Schild coordinates ⓘ |
| usedFor |
Kerr metric
ⓘ
Kerr–Newman metric ⓘ
linked to:
Kerr–Newman black hole
accretion disk modeling around rotating black holes ⓘ frame dragging analysis ⓘ geodesic calculations in Kerr spacetime ⓘ gravitational lensing in Kerr spacetime ⓘ quasinormal mode calculations of rotating black holes ⓘ rotating black hole spacetime ⓘ stationary axisymmetric spacetimes ⓘ |
| usedIn | general relativity ⓘ |
| yearIntroduced | 1967 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Boyer–Lindquist coordinates Description of subject: Boyer–Lindquist coordinates are a spheroidal coordinate system commonly used in general relativity to express the Kerr solution describing the spacetime around a rotating black hole.
Referenced by (11)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Boyer–Lindquist coordinates
linked to: Boyer–Lindquist coordinates
linked to: Boyer–Lindquist coordinates
linked to: Boyer–Lindquist coordinates