Horizon states for AdS black holes

We study the time-independent modes of a massless scalar field in various b lack-hole backgrounds, and show that for these black holes, the time-indepe ndent mode is localized at the horizon. A similar analysis is done for time -independent. equilibrium modes of the five-dimensional plane AdS black hol e. A self-adjointness analysis of this problem reveals that in addition to the modes corresponding to the usual glueball states, there is a discrete i nfinity of other equilibrium modes with imaginary mass for the glueball. We suggest: these modes may be related to a Savvidy-Nielsen-Olesen-like vacuu m instability in QCD. (C) 2000 Elsevier Science B.V. All rights reserved.