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- Title
Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime.
- Authors
Baines, Joshua; Berry, Thomas; Simpson, Alex; Visser, Matt
- Abstract
Recently, the current authors have formulated and extensively explored a rather novel Painlevé–Gullstrand variant of the slow-rotation Lense–Thirring spacetime, a variant which has particularly elegant features—including unit lapse, intrinsically flat spatial 3-slices, and a separable Klein–Gordon equation (wave operator). This spacetime also possesses a non-trivial Killing tensor, implying separability of the Hamilton–Jacobi equation, the existence of a Carter constant, and complete formal integrability of the geodesic equations. Herein, we investigate the geodesics in some detail, in the general situation demonstrating the occurrence of "ultra-elliptic" integrals. Only in certain special cases can the complete geodesic integrability be explicitly cast in terms of elementary functions. The model is potentially of astrophysical interest both in the asymptotic large-distance limit and as an example of a "black hole mimic", a controlled deformation of the Kerr spacetime that can be contrasted with ongoing astronomical observations.
- Subjects
GEODESICS; KLEIN-Gordon equation; ASTRONOMICAL observations; GRAVITATIONAL fields; BLACK holes
- Publication
Universe (2218-1997), 2022, Vol 8, Issue 2, pN.PAG
- ISSN
2218-1997
- Publication type
Article
- DOI
10.3390/universe8020115