Quantum generation of Schwarzschild-de Sitter (Nariai) black holes in effective dilaton-Maxwell gravity

Dilaton coupled electromagnetic field is essential element of low-energy st ring effective action or it may be considered as result of spherical compac tification of Maxwell theory in higher dimensions. The large N and large cu rvature effective action for N dilaton coupled vectors is calculated, Addin g such quantum correction to classical dilaton gravity action we show that effective dilaton-Maxwell gravity under consideration may generate Schwarzs child-de Sitter black holes (SdS BHs) with constant dilaton as solutions of the theory. That suggests a mechanism (alternative to BHs production) for quantum generation of SdS BHs in early universe (actually, for quantum crea tion of inflationary Universe) due to back-reaction of dilaton coupled matt er. The possibility of proliferation of anti-de Sitter space is briefly dis cussed. (C) 1998 Published by Elsevier Science B.V. All rights reserved.