Lie Symmetries of Einstein's Vacuum Equations in N Dimensions
- 10.2991/jnmp.1922.214.171.124How to use a DOI?
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.
- © 2006, the Authors. Published by Atlantis Press.
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- 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.19126.96.36.199 DO - 10.2991/jnmp.19188.8.131.52 ID - Marchildon1998 ER -