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Lie Symmetries of Einstein’s Vacuum Equations inNDimensions

 

作者: Louis Marchildon,  

 

期刊: Journal of Nonlinear Mathematical Physics  (Taylor Available online 1998)
卷期: Volume 5, issue 1  

页码: 68-81

 

ISSN:1402-9251

 

年代: 1998

 

DOI:10.2991/jnmp.1998.5.1.7

 

出版商: Taylor & Francis Group

 

数据来源: Taylor

 

摘要:

We investigate Lie symmetries of Einstein’s vacuum equations inNdimensions, 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.

 

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