Higher Spin Black Holes with Soft Hair

Abstract

We construct a new set of boundary conditions for higher spin gravity, inspired by a recent "soft Heisenberg hair"-proposal for General Relativity on three-dimensional Anti-de Sitter. The asymptotic symmetry algebra consists of a set of affine $\hat{u}(1)$ current algebras. Its associated canonical charges generate higher spin soft hair. We focus first on the spin-3 case and then extend some of our main results to spin-$N$, many of which resemble the spin-2 results: the generators of the asymptotic $W_3$ algebra naturally emerge from composite operators of the $\hat{u}(1)$ charges through a twisted Sugawara construction; our boundary conditions ensure regularity of the Euclidean solutions space independently of the values of the charges; solutions, which we call "higher spin black flowers", are stationary but not necessarily spherically symmetric. Finally, we derive the entropy of higher spin black flowers, and find that for the branch that is continuously connected to the BTZ black hole, it depends only on the affine purely gravitational zero modes. Using our map to $W$-algebra currents we recover well-known expressions for higher spin entropy. We also address higher spin black flowers in the metric formalism and achieve full consistency with previous results.

24 pages, no figures

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Cited by in corpus (8)

• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Generic AdS3 Black Holes
• Log corrections to entropy of three dimensional black holes with soft hair
• Kerr-Newman Black Hole Entropy and Soft Hair
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• New entropy formula for Kerr black holes
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography