Three-dimensional Einstein gravity with negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near horizon region of these black holes that lead to a surprisingly simple near horizon symmetry algebra consisting of two affine u(1) current algebras. The symmetry algebra is essentially equivalent to the Heisenberg algebra. The associated charges give a specific example of "soft hair" on the horizon, as defined by Hawking, Perry and Strominger. We show that soft hair does not contribute to the Bekenstein-Hawking entropy of Banados-Teitelboim-Zanelli black holes and "black flower" generalizations. From the near horizon perspective the conformal generators at asymptotic infinity appear as composite operators, which we interpret in the spirit of black hole complementarity. Another remarkable feature of our boundary conditions is that they are singled out by requiring that the whole spectrum is compatible with regularity at the horizon, regardless the value of the global charges like mass or angular momentum. Finally, we address black hole microstates and generalizations to cosmological horizons.Comment: 6p

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.Comment: 22 pp, v2: added ref

We present the first example of a nontrivial higher spin theory in three-dimensional flat space. We propose flat-space boundary conditions and prove their consistency for this theory. We find that the asymptotic symmetry algebra is a (centrally extended) higher spin generalization of the Bondi-Metzner-Sachs algebra, which we describe in detail. We also address higher spin analogues of flat space cosmology solutions and possible generalizations.

We provide the first steps toward a flat space holographic correspondence in two bulk spacetime dimensions. The gravity side is described by a conformally transformed version of the matterless Callan-Giddings-Harvey-Strominger model. The field theory side follows from the complex Sachdev-Ye-Kitaev model in the limit of large specific heat and vanishing compressibility. We derive the boundary action analogous to the Schwarzian as the key link between gravity and field theory sides and show that it coincides with a geometric action discovered recently by one of us [