BTZ Black Hole as Solution of 3d Higher Spin Gauge Theory

TL;DR

This work demonstrates that the BTZ black hole is an exact solution of three-dimensional higher-spin gauge theory, formulated via a flat $sp(2)\oplus sp(2)$ connection and the star-product oscillator formalism. By constructing the BTZ gauge function and employing unfolded dynamics on a Fock module, the authors reproduce explicit, massless scalar and spinor solutions in the BTZ background, including the extremal case with Whittaker-function behavior. They analyze how BTZ identifications break the original HS symmetry down to residual subalgebras (typically $u(1)\oplus u(1)$, with $gl(2)$ enhancement in the non-rotating limit) and reveal symmetry enhancements for special parameter values, as well as an extra Killing spinor in the extremal case. The paper lays a path for extending these HS techniques to higher-dimensional Kerr-like systems and to generalized matrix-coordinate spaces, highlighting the utility of the star-product and Fock-module formalisms for black-hole physics in HS theories.

Abstract

BTZ black hole is interpreted as exact solution of 3d higher spin gauge theory. Solutions for free massless fields in BTZ black hole background are constructed with the help of the star-product algebra formalism underlying the formulation of 3d higher spin theory. It is shown that a part of higher spin symmetries remains unbroken for special values of the BTZ parameters.