Studies of the asymptotic structure in classical General Relativity are concerned with the behaviour of the gravitational field at large scales, aiming to identify a large class of spacetimes that share fundamental properties, e.g., symmetries or conserved quantities.

The notion of asymptotically simple spacetimes, referring to spacetimes that resemble Minkowski at large null distances, was central in identifying the infinite-dimensional symmetry group at null infinity, known as the BMS group. The BMS group is the semi-direct product of the Lorentz group with the infinite-dimensional group of angle-dependent translations along null infinity. Associated with these symmetries is an infinite number of BMS asymptotic charges. In recent collaborative work, we analyse BMS asymptotic charges in the context of an initial value problem. Our results indicate that BMS asymptotic charges are not well-defined in the limit of spatial infinity for generic initial data unless the initial data satisfy extra regularity conditions. This research strategy offers a promising avenue for investigating different research problems, such as the gravitational memory effect.

The gravitational memory effect emerged as an exciting research avenue, partly due to its relation with gravitational waves, the information loss paradox and its connection to BMS asymptotic symmetries. Simply put, the gravitational memory effect refers to the residual effect on a gravitational wave detector after the passage of a gravitational wave. During my stay at ESI, my focus will revolve around the gravitational memory effects in the context of an initial value problem of the field equations. The goal is to explore the relationship between gravitational memory and the properties of initial data on a Cauchy hypersurface. This analysis is motivated by recent work by Garfinkle, suggesting that gravitational memory can be derived from the structure of the source of the wave equations on Minkowski spacetime.