Killing Tensor and Carter Constant for Painlevé–Gullstrand Form of Lense–Thirring Spacetime

@article{Baines2021KillingTA,
  title={Killing Tensor and Carter Constant for Painlev{\'e}–Gullstrand Form of Lense–Thirring Spacetime},
  author={Joshua Baines and Thomas Berry and Alex Simpson and Matt Visser},
  journal={Universe},
  year={2021}
}
Recently, the authors have formulated and explored a novel Painlevé–Gullstrand variant of the Lense–Thirring spacetime, which has some particularly elegant features, including unit-lapse, intrinsically flat spatial 3-slices, and some particularly simple geodesics—the “rain” geodesics. At the linear level in the rotation parameter, this spacetime is indistinguishable from the usual slow-rotation expansion of Kerr. Herein, we shall show that this spacetime possesses a nontrivial Killing tensor… 

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