A class of integrable metrics
Anabalon
A
author
Batista
C
author
2016
English
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.
WOS:000373107300004
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text
files/594_Anabalon+Batista2016.pdf
10.1103/PhysRevD.93.064079
Anabalon+Batista2016
Physical Review D
Phys. Rev. D
2016
Amer Physical Soc
continuing
periodical
academic journal
93
6
13 pp
2470-0010