  We examine the properties of Quantum nonthermal radiation of a Kerr-anti-de
Sitter (KAdS) black holes. Assuming that a crossing of the positive and
negative Dirac energy levels occurs in a region near the event horizon of the
hole, and spontaneous quantum nonthermal radiation takes place in the overlap
region. We solve the biquadratic equation governing the location of the event
horizon of the KAdS black holes and present closed analytic expression for the
radii of the horizons.
