Studies of Asymptotic Symmetries at Null and Spatial Infinity

Abstract

In this thesis we study the relationship between Asymptotic symmetry group of (Asymptotically flat) space-times at Null and Spatial Infinity. We first review the basic framework concerning Null and Spatial Infinity and then discuss the notion of asymptotic symmetry groups in these two regimes. Former is known as the BMS group and the latter is known as SPI group developed by Ashtekar and Hansen\cite{ashtekarhansen}. Based on the formalism developed by Campiglia et al.\cite{campigliaalokmain} we then develop an approach to extend the BMS group at Null infinity to Spatial infinity. For so-called super translation subgroup of the BMS, we see how this extension precisely matches the corresponding supertranslation subgroup of the SPI group. As both the BMS and SPI groups are (semi-direct) products of super-translation groups with Lorentz group, our work shows how the SPI group is just a manifestation of BMS at spatial infinity.