Asymptotic Symmetries of Spacetime and Memory Effect

Abstract

The work presented in this thesis can be broadly divided into two parts: In the first part, we study asymptotic symmetry groups using (i) Gauge-fixing approach and (ii) Geometric approach. The Gauge-fixing approach has been studied extensively for Bondi-Metzner-Sachs (BMS) group as well as some extended definitions, including how to construct symmetry group near event horizon. We have also presented a derivation for Barnich-Troessaert group for asymptotically AdS_d space-times and a possible extended BMS group using Geometric approach. Using such symmetry groups as boundary conditions, we present a general recipe to construct perturbative shock waves on a background curved space-time. In the second part, we implant such shock wave on Schwarzschild and Rindler horizon and look at their classical and semi-classical memory effects. For semi-classical case, we have considered a free mass-less scalar quantum field on Rindler space-time. As noted in previous work [1], super-translation produced by shock-waves can produce mode mixing and particle creation. In this work, we find that super-rotation sub-group can only affect mode-mixing and does not contribute to particle creation. Consequently, the entanglement production between positive frequency modes in right wedge of Rindler space-time is not affected by super-rotation.