Horizon Shells and BMS-like Soldering Transformations

TL;DR

This paper explores the complex structure of null shells at black hole horizons, revealing infinite-dimensional soldering transformations, their relation to Carrollian symmetries, and connections to BMS supertranslations, with detailed analysis of Schwarzschild horizons.

Contribution

It demonstrates the rich classical structure of horizon shells, characterizes the infinite-dimensional soldering transformations, and links horizon shell properties to BMS supertranslation charges.

Findings

Infinite-dimensional soldering group at horizons.

Explicit horizon shell energy-momentum tensor derived.

Conserved shell-energy analogous to BMS supertranslation charges.

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.