Higher Spin Black Holes in Three Dimensions: Comments on Asymptotics and Regularity

TL;DR

This paper investigates the regularity and asymptotic properties of higher spin black holes in three-dimensional Chern-Simons theory, revealing that holonomy conditions alone are insufficient for regularity and that turning on chemical potentials alters asymptotics.

Contribution

It provides a comprehensive analysis of regularity conditions, demonstrates the limitations of holonomy constraints, and shows how chemical potentials affect asymptotic behavior in higher spin black holes.

Findings

Holonomy conditions are necessary but not sufficient for regularity.

Regularity requires turning on chemical potentials, changing asymptotics.

Asymptotics deviate from Brown-Henneaux when chemical potentials are introduced.

Abstract

In the context of (2+1)--dimensional SL(N,R)\times SL(N,R) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metric-like higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turn on -- as demanded by regularity -- the asymptotics cannot be that of Brown-Henneaux.