A BISOGNANO-WICHMANN-LIKE THEOREM IN A CERTAIN CASE OF A NON-BIFURCATE EVENT HORIZON RELATED TO AN EXTREME REISSNER-NORDSTROM BLACK-HOLE

Thermal Wightman functions of a massless scalar field are studied with in the framework of a 'near horizon' static background model of an ext remal R-N black hole. This model is built up by using global Carter-li ke coordinates over an infinite set of Bertotti-Robinson submanifolds glued together. The analytical extendibility beyond the horizon is imp osed as constraints on (thermal) Wightman's functions defined on a Ber totti-Robinson submanifold. It turns out that only the Bertotti-Robins on vacuum state, i.e. T = 0, satisfies the above requirement. Furtherm ore, the extension of this state onto the whole manifold is proved to coincide exactly with the vacuum state in the global Carter-like coord inates. Hence a theorem similar to the Bisognano-Wichmann theorem for the Minkowski spacetime in terms of Wightman functions holds with vani shing 'Unruh-Rindler temperature'. Furthermore, the Carter-like vacuum restricted to a Bertotti-Robinson region, resulting in a pure state t here, has vanishing entropy despite the presence of event horizons. So me comments on the real extremal R-N black hole are given.