Boundary Charges at Null Infinity; Asymptotic symmetries, Memory effects and Conformal Structure

Abstract

This thesis studies the geometry of asymptotically flat spacetimes with null infinity as the primary arena for gravitational radiation and observables. Using Bondi–Sachs and conformal Gaussian null coordinates, it analyses the BMS symmetry group, flux–balance laws, and the gravitational memory effect. The work examines the supertranslation ambiguity in angular momentum, discusses recent quasilocal correction terms linking the shear potential to the Bondi mass aspect. In addition to the theoretical analysis, a suite of computational tools has been developed using the xAct tensor algebra framework in Mathematica. These implementations reproduce and extend BMS calculations for four-dimensional asymptotically flat spacetimes and provide a flexible platform for exploring analogous structures in higher dimensions, where the asymptotic symmetry structure differs qualitatively from the four-dimensional case. Future directions include a conformal GHP treatment for a more geometrical view point intrinsic to J, with gauge independence.