2015/10/22 by Suhail Khan, Khan, Suhail, Tahir Hussain +19
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1510.06776
In this paper, we investigate conformal Killing's vectors (CKVs) admitted by\nsome plane symmetric spacetimes. Ten conformal Killing's equations and their\ngeneral forms of CKVs are derived along with their conformal factor. The\nexistence of conformal Killing's symmetry imposes restrictions on the metric\nfunctions. The conditions imposing restrictions on these metric functions are\nobtained as a set of integrability conditions. Considering the cases of\ntime-like and inheriting CKVs, we obtain spacetimes admitting plane conformal\nsymmetry. Integrability conditions are solved completely for some known\nnon-conformally flat and conformally flat classes of plane symmetric\nspacetimes. A special vacuum plane symmetric spacetime is obtained, and it is\nshown that for such a metric CKVs are just the homothetic vectors (HVs). Among\nall the examples considered, there exists only one case with a six dimensional\nalgebra of special CKVs admitting one proper CKV. In all other examples of\nnon-conformally flat metrics, no proper CKV is found and CKVs are either HVs or\nKilling's vectors (KVs). In each of the three cases of conformally flat\nmetrics, a fifteen dimensional algebra of CKVs is obtained of which eight are\nproper CKVs.\n