Abstract
The extreme Reissner–Nordström black holes have zero surface gravity. However, a semiclassical analysis seems to be ill-defined for these objects and apparently no notion of temperature exists for them. It is conjectured that these properties may be shared for all kind of black holes whose surface gravity is zero. Two examples are worked out explicitly: the scalar–tensor cold black holes and extreme black holes resulting from a gravity system coupled to a generalized Maxwell field in higher dimensions. The reasons for this anomolous behavior are discussed as well as its thermodynamics implications.
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