Higher spin black holes in three dimensions: Remarks on asymptotics and regularity

In the context of (2 + 1)-dimensional SL(N, R) x 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 metriclike 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 turned on-as demanded by regularity-the asymptotics cannot be that of Brown-Henneaux.