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Abstract |
In four dimensions, the most general metric admitting two commuting Killing vectors and a rank-two Killing tensor can be parametrized by ten arbitrary functions of a single variable. We show that picking a special vierbein, reducing the system to eight functions, implies the existence of two geodesic and share-free, null congruences, generated by two principal null directions of the Weyl tensor. Thus, if the spacetime is an Einstein manifold, the Goldberg-Sachs theorem implies it is Petrov type D, and by explicit construction, is in the Carter class. Hence, our analysis provides a straightforward connection between the most general integrable structure and the Carter family of spacetimes. |
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Address |
[Anabalon, Andres] Univ Adolfo Ibanez, Dept Ciencias, Fac Artes Liberales, Ave Padre Hurtado 750, Vina Del Mar, Chile, Email: andres.anabalon@uai.cl; |
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