# Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions

## Abstract

We study the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-(Anti) de Sitter black hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black hole rotation parameters. We analyze explicitly the symmetry properties of these backgrounds that allow for this Liouville integrability and construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties. This work greatly generalizes previously known results for both the Myers-Perry metrics, and the Kerr-(Anti) de Sitter metrics in higher dimensions.

- Authors:

- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2J1 (Canada)
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1 (Canada)

- Publication Date:

- OSTI Identifier:
- 20774529

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.72.124008; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; DE SITTER GROUP; EQUATIONS OF MOTION; HAMILTON-JACOBI EQUATIONS; KLEIN-GORDON EQUATION; METRICS; ROTATION; SCALAR FIELDS; SPACE-TIME; SYMMETRY

### Citation Formats

```
Vasudevan, Muraari, and Stevens, Kory A.
```*Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.124008.

```
Vasudevan, Muraari, & Stevens, Kory A.
```*Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions*. United States. doi:10.1103/PhysRevD.72.124008.

```
Vasudevan, Muraari, and Stevens, Kory A. Thu .
"Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions". United States.
doi:10.1103/PhysRevD.72.124008.
```

```
@article{osti_20774529,
```

title = {Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions},

author = {Vasudevan, Muraari and Stevens, Kory A.},

abstractNote = {We study the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-(Anti) de Sitter black hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black hole rotation parameters. We analyze explicitly the symmetry properties of these backgrounds that allow for this Liouville integrability and construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties. This work greatly generalizes previously known results for both the Myers-Perry metrics, and the Kerr-(Anti) de Sitter metrics in higher dimensions.},

doi = {10.1103/PhysRevD.72.124008},

journal = {Physical Review. D, Particles Fields},

number = 12,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}