Static BPS black hole in 4d higher-spin gauge theory

TL;DR

This paper constructs an exact static BPS black-hole solution in 4d higher-spin gauge theory with N=2 supersymmetry, described by a single mass parameter $M$ and BH charge $e$. Using the unfolded formulation and a Killing-symmetry–based Fock-vacuum in the HS star-product algebra, the authors reduce the nonlinear problem to tractable 3d HS equations and show that nonlinear corrections cancel for the static configuration, yielding a solution that preserves $1/4$ of the supersymmetry. In the weak-field limit, the solution contains the $AdS_4$ Schwarzschild BH in the spin-2 sector along with an infinite tower of massless higher-spin fields; in the full nonlinear theory it remains BPS and is encoded by explicit expressions for the HS fields $S$, $B$, and $W$. The results reveal a deep link between higher-spin dynamics and lower-dimensional HS structures, suggest extremality, and open avenues for generalizations to rotating, NUT, and higher-dimensional BHs, as well as investigations of horizons, thermodynamics, and fluctuations in HS backgrounds.

Abstract

We find exact spherically symmetric solution of 4d nonlinear bosonic higher-spin gauge theory, that preserves a quarter of supersymmetries of N=2 supersymmetric 4d higher-spin gauge theory. In the weak field regime it describes $AdS_4$ Schwarzschild black hole in the spin two sector along with non-zero massless fields of all integer spins.