Dilaton black holes in grand canonical ensemble near the extreme state
O. B. Zaslavskii
Abstract
Dilaton black holes with a pure electric charge are considered in a framework of a grand canonical ensemble near the extreme state. It is shown that there exists such a subset of boundary data that the Hawking temperature smoothly goes to zero to an infinite value of a horizon radius but the horizon area and entropy are finite and differ from zero. In string theory the existence of a horizon in the extreme limit is due to the finiteness of a system only.
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