Spacetime structure near generic horizons and soft hair

TL;DR

The paper develops a general, dimension-agnostic framework for non-extremal horizons, showing how different boundary conditions at the horizon induce infinite-dimensional near-horizon symmetries. It identifies two main algebraic structures: a linear BMS-like family labeled by spin-$s$ and a nonlinear Heisenberg-like family, with the former emergent as composites of the latter. The analysis yields explicit Kerr and Kerr–Taub–NUT realizations, clarifies soft hair contributions to entropy, and discusses ensemble dependence via boundary data. The work suggests soft hair on cosmological horizons and potential links to thermodynamics and information-related questions in black hole physics.

Abstract

We explore the spacetime structure near non-extremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. 2. The near horizon algebra of a set of boundary conditions, labeled by a parameter $s$, is given by the semi-direct sum of diffeomorphisms at the horizon with "spin-$s$ supertranslations". For $s=1$ we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. 3. For another choice, we find a non-linear extension of the Heisenberg algebra, generalizing recent results in three spacetime dimensions. This algebra allows to recover the aforementioned (linear) ones as composites. 4. These examples allow to equip not only black holes, but also cosmological horizons with soft hair. We also discuss implications of soft hair for black hole thermodynamics and entropy.