Journal of Nonlinear Mathematical Physics

Volume 5, Issue 1, February 1998, Pages 68 - 81

Lie Symmetries of Einstein's Vacuum Equations in N Dimensions

Authors
Louis Marchildon
Corresponding Author
Louis Marchildon
Received 20 January 1997, Accepted 14 October 1997, Available Online 1 February 1998.
DOI
10.2991/jnmp.1998.5.1.7How to use a DOI?
Abstract

We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein's equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstein's equations), we set to zero the coefficients of derivatives that do not appear in Einstein's equations. This considerably constrains the coefficients of symmetry generating vector fields. Using the Lie algebra property of generators of symmetries and the fact that general coordinate transformations are symmetries of Einstein's equations, we are then able to obtain all the Lie symmetries. The method we have used can likely be applied to other types of equations.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
5 - 1
Pages
68 - 81
Publication Date
1998/02/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.1998.5.1.7How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Louis Marchildon
PY  - 1998
DA  - 1998/02/01
TI  - Lie Symmetries of Einstein's Vacuum Equations in N Dimensions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 68
EP  - 81
VL  - 5
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1998.5.1.7
DO  - 10.2991/jnmp.1998.5.1.7
ID  - Marchildon1998
ER  -