Higher Spin Black Holes with Soft Hair

Understand

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.