• DOI:10.3390/universe7120473
• Corpus ID: 238353805

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}
}

• J. Baines, T. Berry, +1 author M. Visser
• Published 5 October 2021
• Physics
• Universe

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, implying separability of the Hamilton–Jacobi equation. Furthermore, we shall show that the Klein–Gordon equation is also separable on this spacetime. However, while the Killing tensor has a 2-form square root, we shall see that this 2-form square root of the Killing tensor is not a Killing–Yano tensor. Finally, the Killing-tensor-induced Carter constant is easily extracted, and now, with a fourth constant of motion, the geodesics become (in principle) explicitly integrable.