Soft hairy horizons in three spacetime dimensions

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.Comment: 22 pp, v2: added ref

New entropy formula for Kerr black holes

“…In this section we review material that appeared in [1,9], whose conventions and notations we use. We start with the near horizon expansion of non-extremal black holes (or cosmologies).…”

“…The near horizon boundary conditions of [1,9] allow for arbitrary variations of the horizon radius function γ and the rotation function ω but no variations of Rindler acceleration α, i.e., δγ 0 δω and δα = 0. For constant Rindler acceleration the equations of motion imply conservation of these functions in time, ∂ t γ = 0 = ∂ t ω, which are near horizon analogs of the holographic Ward identities ∂ ∓ T ±± = 0 for the usual Brown-Henneaux boundary conditions [20].…”

“…During the past 18 months the entropy formula (1) was shown to apply also to flat space cosmologies in Einstein gravity [9], to black holes (flat space cosmologies) in higher spin theories [10] ( [11]) where Bekenstein-Hawking fails, and to higher derivative theories with gravitational Chern-Simons term [12] where Wald's formula fails.…”

“…Besides the entropy itself also Cardyology simplifies [1,9,13] including log-corrections [14], while semi-classical considerations allow for Hardyology [15][16][17][18], by which we mean a counting of explicitly constructed semi-classical black hole microstates that combinatorially reduces to partitions of large integers. Nearly all results so far apply only to three spacetime dimensions, with the exception of [18] that applies Hardyology to extremal Kerr black holes.…”

Near-horizon BMS symmetries as fluid symmetries

“…We will study the fluid interpretation of 3d flat gravity in a companion paper [30]. In the future, it would be interesting to use the fluid perspective to understand the symmetry groups appearing at Rindler horizons [31], with negative cosmological constant [32,33], and in more general theories of gravity (e.g., [34,35]). The remainder of this paper is organized as follows.…”