Lie symmetries for equations in conformal geometries
Abstract
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 May 2005
 DOI:
 10.1088/03054470/38/20/009
 arXiv:
 arXiv:grqc/0504104
 Bibcode:
 2005JPhA...38.4419H
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 19 pages, To appear in J. Phys. A