Spacetime structure near generic horizons and soft hair

TL;DR

This paper investigates the spacetime structure near generic horizons in higher dimensions, revealing new boundary conditions, algebraic structures like BMS and Heisenberg extensions, and implications for soft hair and entropy.

Contribution

It introduces novel boundary conditions and algebraic structures near horizons, extending soft hair concepts to black holes and cosmological horizons in higher dimensions.

Findings

Boundary conditions characterized by a functional of dynamical variables.

Near horizon algebra includes BMS and non-linear Heisenberg extensions.

Soft hair can be assigned to both black holes and cosmological horizons.

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.