Exactly solvable models of two-dimensional dilaton gravity and quantum eternal black holes
Abstract
New approach to exact solvability of dilaton gravity theories is suggested which appeals directly to structure of field equations. It is shown that black holes regular at the horizon are static and their metric is found explicitly. If a metric possesses singularities the whole spacetime can be divided into different sheets with one horizon on each sheet, neighboring sheets being glued along the singularity. The position of singularities coincide with the values of dilaton in solutions with a constant dilaton field. Quantum corrections to the Hawking temperature vanish. For the wide subsets of these models the relationship between the total energy and the total entropy of the quantum finite size system is the same as in the classical limit or, moreover, the metric itself does not acquire quantum corrections. The present paper generalizes Solodukhin's results on the RST model in that instead of the particular model we deal with the whole classes of them. Apart from this, the found models exhibit some qualitatively new properties which are absent in the RST model. The most important one is that there exist quantum black holes with geometry regular everywhere including infinity.Keywords
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