Poincaré coordinates
E590884
Poincaré coordinates are a commonly used coordinate system on anti-de Sitter space that makes its conformal boundary manifestly Minkowskian and is especially convenient in AdS/CFT calculations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Poincaré coordinates canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6396978 — 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: Poincaré coordinates Context triple: [anti-de Sitter space, admitsCoordinateSystem, Poincaré 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.
-
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.
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.
-
D.
Boyer–Lindquist coordinates
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.
-
E.
Kerr–Schild coordinates
Kerr–Schild coordinates are a coordinate system used to express the Kerr spacetime metric in a form that highlights its structure as a perturbation of flat Minkowski space along a principal null direction.
- 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: Poincaré coordinates Target entity description: Poincaré coordinates are a commonly used coordinate system on anti-de Sitter space that makes its conformal boundary manifestly Minkowskian and is especially convenient in AdS/CFT calculations.
-
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.
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.
-
D.
Boyer–Lindquist coordinates
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.
-
E.
Kerr–Schild coordinates
Kerr–Schild coordinates are a coordinate system used to express the Kerr spacetime metric in a form that highlights its structure as a perturbation of flat Minkowski space along a principal null direction.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
coordinate system
ⓘ
mathematical concept ⓘ |
| appearsIn |
quantum gravity in AdS space
ⓘ
string theory on AdS backgrounds ⓘ supergravity solutions on AdS ⓘ |
| associatedWith |
Poincaré group on the boundary
ⓘ
conformal boundary of AdS ⓘ |
| boundaryDimension | d ⓘ |
| boundaryLocatedAt | z = 0 ⓘ |
| boundaryMetric | eta_{ mu u} dx^{ mu} dx^{ u} ⓘ |
| boundarySignature | Minkowski ⓘ |
| bulkRegion | z > 0 ⓘ |
| coordinateRange |
t
in
(-
i
nfty,
+
i
nfty)
ⓘ
x^i in (- i nfty, + i nfty) ⓘ z > 0 ⓘ |
| dimensionConvention | bulk dimension d+1 ⓘ |
| hasBoundaryCoordinates | x^{ mu} ⓘ |
| hasParameter | AdS radius L ⓘ |
| hasProperty |
adapted to AdS/CFT correspondence
ⓘ
conformally flat boundary metric ⓘ covers only a patch of global AdS ⓘ makes conformal boundary manifestly Minkowskian ⓘ often called Poincaré patch coordinates ⓘ |
| hasRadialCoordinate | z ⓘ |
| hasSpatialCoordinates | vec{x} ⓘ |
| hasTimeCoordinate | t ⓘ |
| induces | flat Minkowski metric on the boundary up to a conformal factor ⓘ |
| metricDependsOn | AdS radius L ⓘ |
| metricForm | ds^2 = (L^2/z^2)(dz^2 + eta_{ mu u} dx^{ mu} dx^{ u}) ⓘ |
| namedAfter | Henri Poincaré ⓘ |
| relatedTo |
Fefferman–Graham coordinates
ⓘ
global AdS coordinates ⓘ |
| simplifies |
Fourier transforms along boundary directions
ⓘ
asymptotic analysis near AdS boundary ⓘ identification of boundary field theory ⓘ |
| usedFor |
constructing AdS black brane solutions
ⓘ
finite-temperature AdS/CFT setups ⓘ holographic RG flows ⓘ holographic hydrodynamics ⓘ studying conformal field theories on Minkowski space ⓘ |
| usedIn |
AdS/CFT calculations
ⓘ
Witten diagrams ⓘ
linked to:
Feynman diagrams
bulk-to-boundary propagators ⓘ gauge/gravity duality ⓘ
linked to:
AdS/CFT correspondence
holographic correlation functions ⓘ holographic entanglement entropy ⓘ holographic renormalization ⓘ |
| usedOn |
AdS_{d+1}
ⓘ
anti-de Sitter space ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Poincaré coordinates Description of subject: Poincaré coordinates are a commonly used coordinate system on anti-de Sitter space that makes its conformal boundary manifestly Minkowskian and is especially convenient in AdS/CFT calculations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.