Lie Symmetries of Einstein's Vacuum Equations in N Dimensions

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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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  -