# 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…

## 16 Citations

### Geodesics for the Painlevé–Gullstrand form of Lense–Thirring Spacetime

- Physics, MathematicsUniverse
- 2022

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…

### Constant-r geodesics in the Painlevé–Gullstrand form of Lense–Thirring spacetime

- PhysicsGeneral Relativity and Gravitation
- 2022

Herein we explore the non-equatorial constant-r (“quasi-circular”) geodesics (both timelike and null) in the Painlevé–Gullstrand variant of the Lense–Thirring spacetime recently introduced by the…

### Slowly rotating black holes with exact Killing tensor symmetries

- PhysicsPhysical Review D
- 2022

We present a novel family of slowly rotating black hole solutions in four, and higher dimensions, that extend the well known Lense–Thirring spacetime and solve the field equations to linear order in…

### Painlevé–Gullstrand coordinates versus Kerr spacetime geometry

- PhysicsGeneral Relativity and Gravitation
- 2022

We discuss the tension between the possible existence of Painlevé–Gullstrand coordinate systems versus the explicit geometrical features of the Kerr spacetime; a subject of interest to Professor…

### Charged black-bounce spacetimes

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2021

Given the recent development of rotating black-bounce-Kerr spacetimes, for both theoretical and observational purposes it becomes interesting to see whether it might be possible to construct…

### Killing tensors of a generalized Lense-Thirring spacetime

- PhysicsPhysical Review D
- 2022

We investigate the Hamilton–Jacobi equation of a probe particle moving on d -dimensional generalized Lense-Thirring metric. This spacetime is diﬀerent from the slowly rotating Myers-Perry black hole…

### The eye of the storm: a regular Kerr black hole

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2022

We analyse in some detail a highly tractable non-singular modification of the Kerr geometry, dubbed the “eye of the storm” — a rotating regular black hole with an asymptotically Minkowski core. This…

### Cosmology in Painlevé-Gullstrand coordinates

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2022

Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) “at rest”, while “space” is expanding.…

### Physically motivated ansatz for the Kerr spacetime

- PhysicsClassical and Quantum Gravity
- 2022

Despite some 60 years of work on the subject of the Kerr rotating black hole there is as yet no widely accepted physically based and pedagogically viable ansatz suitable for deriving the Kerr…

### General-relativistic thin-shell Dyson megaspheres

- PhysicsPhysical Review D
- 2022

: Loosely inspired by the somewhat fanciful notion of detecting an arbitrarily advanced alien civilization, we consider a general-relativistic thin-shell Dyson mega-sphere completely enclosing a…

## References

SHOWING 1-10 OF 49 REFERENCES

### Painlevé–Gullstrand form of the Lense–Thirring Spacetime

- PhysicsUniverse
- 2021

The standard Lense–Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular…

### Unit-lapse versions of the Kerr spacetime

- PhysicsClassical and Quantum Gravity
- 2020

The Kerr spacetime is perhaps the most astrophysically important of the currently known exact solutions to the Einstein field equations. Whenever spacetimes can be put in unit-lapse form it becomes…

### Darboux diagonalization of the spatial 3-metric in Kerr spacetime

- Physics
- 2020

The astrophysical importance of the Kerr spacetime cannot be overstated. Of the currently known exact solutions to the Einstein field equations, the Kerr spacetime stands out in terms of its direct…

### Charged black-bounce spacetimes

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2021

Given the recent development of rotating black-bounce-Kerr spacetimes, for both theoretical and observational purposes it becomes interesting to see whether it might be possible to construct…

### The Carter tensor and the physical-space analysis in perturbations of Kerr-Newman spacetime

- Physics
- 2021

The Carter tensor is a Killing tensor of the Kerr-Newman spacetime, and its existence implies the separability of the wave equation. Nevertheless, the Carter operator is known to commute with the…

### Black holes, hidden symmetries, and complete integrability

- PhysicsLiving reviews in relativity
- 2017

It is demonstrated that the principal tensor can be used as a “seed object” which generates all these symmetries of higher-dimensional Kerr–NUT–(A)dS black hole spacetimes and the review contains a discussion of different applications of the developed formalism and its possible generalizations.

### A novel family of rotating black hole mimickers

- Physics
- 2021

The recent opening of gravitational wave astronomy has shifted the debate about black hole mimickers from a purely theoretical arena to a phenomenological one. In this respect, missing a definitive…

### Regular coordinate systems for Schwarzschild and other spherical spacetimes

- Physics
- 2001

The continuation of the Schwarzschild metric across the event horizon is a well-understood problem discussed in most textbooks on general relativity. Among the most popular coordinate systems that…

### Asymptotic expansions of the Cotton–York tensor on slices of stationary spacetimes

- Mathematics
- 2004

We discuss expansions for the Cotton-York tensor near infinity for arbitrary slices of stationary spacetimes. From these expansions, it follows directly that a necessary condition for the existence…

### GEOMETRY OF THE KERR BLACK HOLES

- Physics, Mathematics
- 2017

In this paper, we will explore the geometry of the Kerr spacetime, a solution to the Einstein Equation in general relativity. We will first give physical and mathematical motivations, and sketch the…