Soft hairy horizons in three spacetime dimensions
Hamid Afshar, Daniel Grumiller, Wout Merbis, Alfredo Perez, David Tempo, Ricardo Troncoso
TL;DR
The paper develops a universal near-horizon symmetry framework for three-dimensional gravity, showing that soft hairy horizons in both AdS3 and flat space are governed by infinite copies of the Heisenberg algebra, supplemented by two Casimirs. Through metric and Chern–Simons formalisms, it derives boundary conditions, canonical charges, and the related algebra, demonstrating soft-hair descendent states of equal energy. It connects these NHSA structures to composite algebras such as BMS3, warped conformal, and Virasoro via twisted Sugawara-type constructions, and confirms a consistent entropy picture across macroscopic, microscopic, and thermodynamic viewpoints, with S = 2π(J0^+ + J0^-) and S = A/4G. The results emphasize a remarkable universality of near-horizon physics, persisting across AdS and flat spacetimes, and hint at extensions to higher spins and dimensions. Overall, the work clarifies how soft hair and simple horizon microstate counting emerge from a minimal NHSA, offering a robust framework for horizon thermodynamics and potential holographic descriptions beyond AdS3.
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.