Interpolating Between Asymptotic and Near Horizon Symmetries

TL;DR

This paper introduces a method to connect asymptotic and near horizon symmetries in three-dimensional black holes, enabling the addition of soft hair excitations at the horizon that are undetectable from infinity.

Contribution

It provides a framework to interpolate between different boundary conditions, linking Virasoro and u(1) symmetries in black hole spacetimes.

Findings

Successfully matches boundary conditions at infinity and the horizon.

Enables BTZ black holes to have soft hair excitations.

Provides tools for understanding black hole symmetries and soft hair.

Abstract

We develop basic tools and matching conditions to interpolate between asymptotic and near horizon symmetries. We focus on black holes in three dimensions. In particular, we match Brown--Henneaux boundary conditions at infinity, which yields two Virasoro algebras, to Heisenberg boundary conditions at the horizon yielding two u(1) current algebras. Our construction allows to equip BTZ black holes with soft hair excitations at the horizon invisible to the asymptotic observer.