As Generated By A Killing Tensor
Noether's theorem states that all conserved quantities are related to spacetime symmetries. Carter's constant is related to a higher order symmetry of the Kerr metric generated by a second order Killing tensor field (different than used above). In component form:
-
- ,
where is the four-velocity of the particle in motion. The components of the Killing tensor in Boyer-Lindquist coordinates are:
-
- ,
where are the components of the metric tensor and and are the components of the principal null vectors:
- .
Read more about this topic: Carter Constant
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