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.

Aliases (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 spacetime → stationary axisymmetric spacetimes →
basedOn	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 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 NERFINISHED → 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 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 spacetime → general relativity →

Referenced by (4)

Subject (surface form when different)	Predicate
Boyer–Lindquist coordinates → Kerr–Schild coordinates ("Kerr–Schild form of the metric") →	relatedTo
Kerr–Schild coordinates ("Kerr–Schild ansatz") →	generalizationOf
Kerr metric →	hasCoordinateSystem