# Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes

## Abstract

A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a nonflat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find solutions of the Einstein equations in D-dimensional space-time with D-2 commuting Killing vectors using the complete integrability of this system. The method appears also to be promising for the analysis of the uniqueness questions for higher-dimensional black holes.

- Authors:

- Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia, and Novosibirsk University, 630090, Novosibirsk (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 20776742

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044004; (c) 2006 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; COSMOLOGY; EINSTEIN FIELD EQUATIONS; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; SOLITONS; SPACE-TIME; SYMMETRY; VECTORS

### Citation Formats

```
Pomeransky, A.A..
```*Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.044004.

```
Pomeransky, A.A..
```*Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes*. United States. doi:10.1103/PhysRevD.73.044004.

```
Pomeransky, A.A.. Wed .
"Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes". United States.
doi:10.1103/PhysRevD.73.044004.
```

```
@article{osti_20776742,
```

title = {Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes},

author = {Pomeransky, A.A.},

abstractNote = {A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a nonflat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find solutions of the Einstein equations in D-dimensional space-time with D-2 commuting Killing vectors using the complete integrability of this system. The method appears also to be promising for the analysis of the uniqueness questions for higher-dimensional black holes.},

doi = {10.1103/PhysRevD.73.044004},

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

number = 4,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}

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