Unfolded Description of $AdS_4$ Kerr Black Hole

TL;DR

This work presents a coordinate-free unfolded formulation of the $AdS_4$ Kerr black hole by deforming the $AdS_4$ zero-curvature system with Killing-symmetry data, yielding a Kerr–Schild description embedded in a Killing-based unfolded set of equations. The authors construct the BH Unfolded System (BHUS), derive consistency conditions and Killing projectors, and show how the Kerr-Schild vector and associated fields arise naturally within this framework. They demonstrate that BHUS reproduces Kerr geometry and generates Kerr-Schild massless-field solutions for all spins in $AdS_4$, linking Weyl, Maxwell, and Papapetrou structures to the background geometry. The approach provides a powerful, coordinate-independent route to analyze black holes in the context of higher-spin gauge theory and suggests extensions to complex mass parameters and nonlinear HS dynamics with potential Taub–NUT connections.

Abstract

It is shown that $AdS_4$ Kerr black hole is a solution of simple unfolded differential equations that form a deformation of the zero-curvature description of empty $AdS_4$ space-time. Our construction uses the Killing symmetries of the Kerr solution. All known and some new algebraic properties of the Kerr-Schild solution result from the obtained black hole unfolded system in the coordinate-independent way. Kerr Schild type solutions of free equations in $AdS_4$ for massless fields of any spin, associated to the proposed black hole unfolded system, are found.