Null infinity as a Killing horizon

Abstract

Symmetries are ubiquitous in modern physics. They not only allow for a more simplified description of physical systems but also, from a more fundamental perspective, can be seen as determining a theory itself. In the present paper, we propose a new definition of asymptotic symmetries that unifies and generalizes the usual notions of symmetry considered in asymptotically flat spacetimes and expanding universes with cosmological horizons. This is done by considering BMS-like symmetries for "asymptotic (conformal) Killing horizons", or A(C)KHs, here defined as null hypersurfaces that are tangent to a vector field satisfying the (conformal) Killing equation in a limiting sense. The construction is theory-agnostic and extremely general, for it makes no use of the Einstein equations and can be applied to a wide range of scenarios with different dimensions or hypersurface cross sections. While we reproduce the results by Dappiaggi, Moretti, and Pinamonti in the case of asymptotic Killing horizons, the conformal generalization does not yield only the BMS group, but a larger group. The enlargement is due to the presence of "superdilations". We speculate on many implications and possible continuations of this work, including the exploration of gravitational memory effects beyond general relativity, understanding antipodal matching conditions at spatial infinity in terms of bifurcate horizons, and the absence of superrotations in de Sitter spacetime and Killing horizons.