Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime
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 e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/2/115 |
| _version_ | 1797476213399224320 |
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| author | Joshua Baines Thomas Berry Alex Simpson Matt Visser |
| author_facet | Joshua Baines Thomas Berry Alex Simpson Matt Visser |
| author_sort | Joshua Baines |
| collection | DOAJ |
| description | 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 <i>formal</i> 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. |
| first_indexed | 2024-03-09T20:54:47Z |
| format | Article |
| id | doaj.art-b9514bd2895542dfa03c017d59675327 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T20:54:47Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-b9514bd2895542dfa03c017d596753272023-11-23T22:23:40ZengMDPI AGUniverse2218-19972022-02-018211510.3390/universe8020115Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring SpacetimeJoshua Baines0Thomas Berry1Alex Simpson2Matt Visser3School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New ZealandRobinson Research Institute, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New ZealandSchool of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New ZealandSchool of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New ZealandRecently, 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 <i>formal</i> 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.https://www.mdpi.com/2218-1997/8/2/115Painlevé–Gullstrand metricsLense–Thirring metricKilling tensorCarter constantintegrabilitygeodesics |
| spellingShingle | Joshua Baines Thomas Berry Alex Simpson Matt Visser Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime Universe Painlevé–Gullstrand metrics Lense–Thirring metric Killing tensor Carter constant integrability geodesics |
| title | Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime |
| title_full | Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime |
| title_fullStr | Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime |
| title_full_unstemmed | Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime |
| title_short | Geodesics for the Painlevé–Gullstrand Form of Lense–Thirring Spacetime |
| title_sort | geodesics for the painleve gullstrand form of lense thirring spacetime |
| topic | Painlevé–Gullstrand metrics Lense–Thirring metric Killing tensor Carter constant integrability geodesics |
| url | https://www.mdpi.com/2218-1997/8/2/115 |
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