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Article
Astronomy & Astrophysics
Joshua Baines et al.
Summary: The authors have investigated a novel Painleve-Gullstrand variant of the slow-rotation Lense-Thirring spacetime, which has elegant features such as unit lapse, flat spatial 3-slices, and a separable Klein-Gordon equation. They have explored the geodesics in detail and found the occurrence of ultra-elliptic integrals. They also discovered that the complete integrability of the geodesics can only be explicitly expressed in terms of elementary functions in certain special cases. This model has significant implications in astrophysics and can be used to study the asymptotic large-distance limit and compare with astronomical observations as a mimic of a black hole.
Article
Astronomy & Astrophysics
Matt Visser et al.
Summary: This article discusses the tension between the possible existence of Painleve-Gullstrand coordinate systems and the explicit geometrical features of the Kerr spacetime. It distinguishes between strong and weak Painleve-Gullstrand coordinate systems, and explores what can and cannot be done in these systems. For the Kerr spacetime, the best achievable option seems to be setting the lapse function to unity and representing spatial slices with a factorized unimodular form. The article concludes by examining to what extent this construction can lead to implementing a suitable analogue spacetime model for laboratory simulations of the Kerr spacetime.
GENERAL RELATIVITY AND GRAVITATION
(2022)
Article
Astronomy & Astrophysics
Joshua Baines et al.
Summary: In this article, we explore the non-equatorial constant-r geodesics in the Painleve-Gullstrand variant of the Lense-Thirring spacetime. Despite the lack of spherical symmetry, shells of constant-r geodesics still exist in this spacetime. The determination of the allowed locations and the stability analysis of these geodesics is complex. The angular motion of these geodesics exhibits precession and nutation, typically with incommensurate frequencies. This study is important for understanding physical models similar to the Kerr spacetime.
GENERAL RELATIVITY AND GRAVITATION
(2022)
Article
Astronomy & Astrophysics
Joshua Baines et al.
Summary: The unit-lapse formulations of Kerr spacetime, including the Painleve-Gullstrand form, are strategically important choices for studying the physically crucial but technically challenging Kerr spacetime. Different unit-lapse metrics are useful for examining various geodesics in Kerr spacetime, beyond just the 'rain' geodesics focused on in this article.
CLASSICAL AND QUANTUM GRAVITY
(2021)
Article
Astronomy & Astrophysics
Joshua Baines et al.
Summary: The authors have formulated a novel Painleve-Gullstrand variant of the Lense-Thirring spacetime, which has elegant features such as unit-lapse and intrinsically flat spatial 3-slices. It was found that this spacetime possesses a nontrivial Killing tensor, leading to separability of the Hamilton-Jacobi equation and Klein-Gordon equation. However, the 2-form square root of the Killing tensor is not a Killing-Yano tensor, indicating that further study is required in this area.
Article
Astronomy & Astrophysics
Joshua Baines et al.
Summary: The article discusses a specific variant of the standard Lense-Thirring metric, highlighting its simplicity, clarity, and improved mathematical and physical behavior. By constructing an explicit unit-lapse Painleve-Gullstrand variant of the Lense-Thirring spacetime, it is shown to have flat spatial slices and simple curvature tensors, belonging to Petrov type I. Various characteristics of this Lense-Thirring variant are explored, such as geodesics, ISCOs, and circular photon orbits, with relevance to observational astronomy.
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