### Abstract

A new technique is introduced to investigate the structure of isometry Lie algebras. Some general results are first proved by applying this technique to n-dimensional manifolds equipped with metrics of arbitrary signature. A restriction is then made to 3-manifolds representing the space of orbits of the timelike Killing field in stationary space-times. Under the assumption of asymptotic flatness at spatial infinity, a complete description of isometry Lie algebras of these 3-manifolds is obtained. As corollaries, several results about symmetries of stationary isolated systems in general relativity are proved.

Original language | English (US) |
---|---|

Pages (from-to) | 1567-1572 |

Number of pages | 6 |

Journal | Journal of Mathematical Physics |

Volume | 19 |

Issue number | 7 |

State | Published - Dec 1 1977 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*19*(7), 1567-1572.

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*Journal of Mathematical Physics*, vol. 19, no. 7, pp. 1567-1572.

**A technique for analyzing the structure of isometries.** / Ashtekar, Abhay; Magnon-Ashtekar, Anne.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A technique for analyzing the structure of isometries

AU - Ashtekar, Abhay

AU - Magnon-Ashtekar, Anne

PY - 1977/12/1

Y1 - 1977/12/1

N2 - A new technique is introduced to investigate the structure of isometry Lie algebras. Some general results are first proved by applying this technique to n-dimensional manifolds equipped with metrics of arbitrary signature. A restriction is then made to 3-manifolds representing the space of orbits of the timelike Killing field in stationary space-times. Under the assumption of asymptotic flatness at spatial infinity, a complete description of isometry Lie algebras of these 3-manifolds is obtained. As corollaries, several results about symmetries of stationary isolated systems in general relativity are proved.

AB - A new technique is introduced to investigate the structure of isometry Lie algebras. Some general results are first proved by applying this technique to n-dimensional manifolds equipped with metrics of arbitrary signature. A restriction is then made to 3-manifolds representing the space of orbits of the timelike Killing field in stationary space-times. Under the assumption of asymptotic flatness at spatial infinity, a complete description of isometry Lie algebras of these 3-manifolds is obtained. As corollaries, several results about symmetries of stationary isolated systems in general relativity are proved.

UR - http://www.scopus.com/inward/record.url?scp=36749114270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749114270&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36749114270

VL - 19

SP - 1567

EP - 1572

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 7

ER -