On Spacetime Symmetries in General Relativity and Teleparallel Gravity

Abstract

In this thesis we have investigated Killing, homothetic and conformal Killing vectors for some well known spacetimes. Conformal Killing vectors are in- vestigated for locally rotationally symmetric (LRS) Bianchi type V, static and non static plane symmetric spacetimes in the context of general rel- ativity as well as teleparallel gravity, while Killing and homothetic vec- tors are explored for Kantowski-Sachs, Lemaitre-Tolman-Bondi (LTB) and 3-dimensional static circularly symmetric spacetimes in the framework of teleparallel gravity. In general relativity, it is shown that Bianchi type V, static and non static plane symmetric spacetimes admit proper conformal Killing vectors for some specific values of the metric functions. In teleparallel gravity, it is observed that the LRS Bianchi type V space- times do not admit proper teleparallel conformal Killing vectors. Further, the number of proper teleparallel conformal Killing vectors for static and non static plane symmetric spacetimes turned out to be one or three for different choices of the metric functions. Moreover, it is shown that the Kanstowski-Sachs and LTB metrics do not admit any proper teleparallel homothetic vector. The maximum number of teleparallel Killing vectors for Kantowski-Sachs spacetimes turned out to be seven, while for LTB metric, this maximum number is found to be six. Finally, our analysis shows that the 3-dimensional static circularly sym- metric spacetimes admit a proper teleparallel homothetic vector in only one case, while the maximum number of teleparallel Killing vectors for these spacetimes is found to be six.