Horizon Shells and BMS-like Soldering Transformations

TL;DR

The paper analyzes the freedom to solder two spacetimes along null horizons, showing that when the horizon’s induced metric is invariant along null generators this soldering group is infinite-dimensional, giving rise to horizon shells carrying both matter and impulsive gravitational waves.By formulating the problem in Carrollian terms, it connects horizon-soldering transformations to BMS-like symmetries and identifies conserved shell energies associated with BMS-like supertranslations, suggesting links to black hole hair ideas.Through explicit construction for Schwarzschild in Kruskal coordinates and its Eddington–Finkelstein reformulation, the authors derive closed expressions for the horizon-shell energy-momentum tensor, currents, and gravitational-wave content, along with their conservation laws.These horizon shells generalize Dray–’t Hooft impulses, provide smoothed versions of impulsive waves, and offer a versatile framework for exploring horizon dynamics, holography, and potential connections to horizon hair and near-horizon symmetries.

Abstract

We revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave components. We also rephrase this result in the language of Carrollian symmetry groups. To illustrate this phenomenon we discuss in detail the example of shells on the horizon of the Schwarzschild black hole (with equal interior and exterior mass), uncovering a rich classical structure at the horizon and deriving an explicit expression for the general horizon shell energy-momentum tensor. In the special case of BMS-like soldering supertranslations we find a conserved shell-energy that is strikingly similar to the standard expression for asymptotic BMS supertranslation charges, suggesting a direct relation between the physical properties of these horizon shells and the recently proposed BMS supertranslation hair of a black hole.