On BMS-transformations and the shock wave S-matrix

Abstract

This thesis examines the relation between asymptotic BMS-symmetries and the shock wave S-matrix. After reviewing both formalisms, we see that the shock wave S-matrix in Minkowski space is invariant under supertranslations, which leads to antipodal matching of supertranslation charges between past and future null infinity. We thus identify a simple explicit scattering example of general results found by Strominger and collaborators, which has thus far gone unnoticed in the BMS-literature. For a Schwarzschild black hole, we show that the shift of the event horizon induced by a shock wave satisfies the same relation to the energy-momentum tensor in the two formalisms. This suggests that a description of particle scattering in a black hole background in terms of BMS-charges may be found. We briefly review the derivation of BMS-like symmetries acting at the event horizon of a black hole and show that the Dray-'t Hooft shock wave in tortoise coordinates generates a non-zero horizon superrotation charge. As the BMS-description of black holes is still under development, further exploration of the relation between the two formalisms is deferred to future research.