Kerr–Schild coordinates

E77413

coordinate system general relativity concept

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.

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All labels observed (3)

Label	Occurrences
Kerr–Schild coordinates canonical	2
Kerr–Schild ansatz	1
Kerr–Schild form of the metric	1

Statements (48)

Predicate	Object
instanceOf	coordinate system ⓘ general relativity concept ⓘ
advantage	avoids coordinate singularity at the event horizon ⓘ linearizes some aspects of Einstein equations on a flat background ⓘ simplifies expression of curvature tensors ⓘ
appliesTo	Kerr–Newman black hole ⓘ surface form: Kerr–Newman spacetime stationary axisymmetric spacetimes ⓘ
basedOn	Minkowski space-time ⓘ surface form: Minkowski spacetime
containsTerm	Minkowski metric η_{μν} ⓘ null vector field l_{μ} ⓘ scalar function H ⓘ
coordinateComponents	azimuthal angle φ ⓘ polar angle θ ⓘ radial coordinate r ⓘ time coordinate t ⓘ
emphasizes	perturbation of flat Minkowski space ⓘ principal null direction ⓘ
field	black hole physics ⓘ gravitational physics ⓘ mathematical physics ⓘ
generalizationOf	Kerr–Schild coordinates self-linksurface differs ⓘ surface form: Kerr–Schild ansatz
hasProperty	adapted to a principal null congruence ⓘ can be written in ingoing form ⓘ can be written in outgoing form ⓘ metric determinant equal to Minkowski determinant ⓘ metric written as flat metric plus null term ⓘ penetrating coordinates across the horizon ⓘ regular on the outer event horizon of Kerr black holes ⓘ simplifies Einstein field equations for Kerr spacetime ⓘ
metricForm	g_{μν} = η_{μν} + 2H l_{μ} l_{ν} ⓘ
namedAfter	Alfred Schild ⓘ Roy Kerr ⓘ
nullVectorProperty	l_{μ} is null with respect to g_{μν} ⓘ l_{μ} is null with respect to η_{μν} ⓘ
relatedTo	Boyer–Lindquist coordinates ⓘ Eddington–Finkelstein coordinates ⓘ Kerr metric ⓘ Kerr–Schild coordinates self-linksurface differs ⓘ surface form: Kerr–Schild form of the metric null tetrad formalism ⓘ
usedFor	analytical calculations of geodesics in Kerr spacetime ⓘ constructing exact solutions via Kerr–Schild metrics ⓘ expressing the Kerr metric ⓘ highlighting Kerr spacetime structure ⓘ numerical relativity simulations of Kerr black holes ⓘ studying causal structure near Kerr horizons ⓘ studying rotating black holes ⓘ
usedIn	Kerr metric ⓘ surface form: Kerr spacetime general relativity ⓘ

How these facts were elicited

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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
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Input

Subject: Kerr–Schild coordinates
Description of subject: 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.

Referenced by (4)

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

Kerr metric → hasCoordinateSystem → Kerr–Schild coordinates ⓘ

Boyer–Lindquist coordinates → relatedTo → Kerr–Schild coordinates ⓘ

Kerr–Schild coordinates → relatedTo → Kerr–Schild coordinates self-linksurface differs ⓘ

this entity surface form: Kerr–Schild form of the metric

Kerr–Schild coordinates → generalizationOf → Kerr–Schild coordinates self-linksurface differs ⓘ

this entity surface form: Kerr–Schild ansatz