Gravitational Memory Beyond Null Infinity through Finite-Distance Carrollian Screens
We investigate gravitational memory beyond null infinity by studying finite-distance null hypersurfaces endowed with Carrollian geometry. We show that the intrinsic degenerate geometry, optical data, and null Brown--York tensor of a finite null screen define a quasilocal Carrollian dissipative system, providing a natural framework to characterize the residual geometric response after the passage of radiation. To make this construction explicit and compare it with the standard asymptotic description, we use Robinson--Trautman spacetimes as an exactly solvable radiative setting. For asymptotically flat Robinson--Trautman geometries, we transform the solution to Bondi gauge and extract the asymptotic data directly in terms of the Robinson--Trautman field. In the linearized sector, the Bondi shear is purely electric and produces the standard displacement-memory effect associated with the relaxation toward the final Schwarzschild geometry. We show that the leading large-radius tracefree component of the finite-screen memory reduces to the Bondi displacement memory, while finite-distance corrections retain additional focusing, embedding dependence, angular drift, Coulombic data, and near-zone information. Thus, Bondi memory emerges as the universal asymptotic projection of a broader quasilocal Carrollian response. Late-time screens approaching the final Schwarzschild horizon exhibit exponentially decaying non-isotropic Carrollian data, leaving only the isotropic null Brown--York stress. As a by-product, we construct the Robinson--Trautman solution with nonzero cosmological constant to second order in the radiative amplitude and use the holographic dictionary to study the associated energy fluxes and find that the resulting charge does not obey a universal monotonicity property.