Soft hairy horizons in three spacetime dimensions

TL;DR

This paper explores soft hairy horizons in three-dimensional spacetimes, revealing infinite-dimensional asymptotic symmetries, novel entropy insights, and connections to boundary conditions like the Korteweg-de Vries hierarchy.

Contribution

It introduces new soft hairy cosmologies, derives their metrics, and links asymptotic symmetries to Heisenberg and BMS algebras, with a microscopic entropy formula fitting the results.

Findings

Asymptotic symmetries are governed by infinite Heisenberg algebras.

Bondi-Metzner-Sachs algebra arises from affine u(1) currents.

Microscopic entropy formula matches macroscopic results.

Abstract

We discuss some aspects of soft hairy black holes and a new kind of "soft hairy cosmologies", including a detailed derivation of the metric formulation, results on flat space, and novel observations concerning the entropy. Remarkably, like in the case with negative cosmological constant, we find that the asymptotic symmetries for locally flat spacetimes with a horizon are governed by infinite copies of the Heisenberg algebra that generate soft hair descendants. It is also shown that the generators of the three-dimensional Bondi-Metzner-Sachs algebra arise from composite operators of the affine u(1) currents through a twisted Sugawara-like construction. We then discuss entropy macroscopically, thermodynamically and microscopically and discover that a microscopic formula derived recently for boundary conditions associated to the Korteweg-de Vries hierarchy fits perfectly our results for entropy and ground state energy. We conclude with a comparison to related approaches.