Carter constant
E788877
The Carter constant is a conserved quantity in general relativity that allows the complete integrability of geodesic motion in the Kerr spacetime around a rotating black hole.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
conserved quantity
ⓘ
constant of motion ⓘ hidden symmetry ⓘ physical quantity ⓘ |
| appearsIn |
Hamilton–Jacobi formalism
NERFINISHED
ⓘ
Kerr metric analysis ⓘ geodesic equations in Boyer–Lindquist coordinates ⓘ |
| appliesTo |
geodesic motion
ⓘ
photon trajectories ⓘ test particle motion ⓘ |
| arisesFrom | second-rank Killing tensor ⓘ |
| associatedWith |
Killing tensor symmetry
ⓘ
rotating black holes ⓘ |
| category |
Black hole physics
ⓘ
Conservation laws ⓘ General relativity NERFINISHED ⓘ Mathematical physics ⓘ |
| definedIn | Kerr spacetime NERFINISHED ⓘ |
| dependsOn |
particle four-momentum
ⓘ
polar angle coordinate ⓘ spacetime metric ⓘ |
| discoveredBy | Brandon Carter NERFINISHED ⓘ |
| distinctFrom |
azimuthal angular momentum
ⓘ
energy ⓘ |
| enables |
complete integrability of geodesic equations
ⓘ
separation of geodesic equations ⓘ separation of the Hamilton–Jacobi equation ⓘ |
| field | general relativity NERFINISHED ⓘ |
| generalizes | total angular momentum squared in spherically symmetric spacetimes ⓘ |
| independentOf |
azimuthal coordinate
ⓘ
time coordinate ⓘ |
| mathematicalForm | quadratic in momenta ⓘ |
| namedAfter | Brandon Carter NERFINISHED ⓘ |
| relatedTo |
angular momentum conservation
ⓘ
energy conservation ⓘ integrability of dynamical systems ⓘ |
| usedFor |
classifying bound orbits around Kerr black holes
ⓘ
ray-tracing in Kerr spacetime ⓘ studying black hole accretion flows ⓘ studying gravitational wave sources from extreme mass-ratio inspirals ⓘ |
| validIn | stationary axisymmetric vacuum solutions ⓘ |
| yearProposed | 1968 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.