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 between neighboring singularities with a finite value of dilaton field (addition horizons may arise at infinite value of it), 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 a wide subset 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. For another subset the metric itself does not acquire quantum corrections. The present paper generalizes Solodukhin's results on the RST model in that instead of a particular model we deal with 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.

22 pages of text plus 2 figures, RevTeX. In new version material on Liouville theory and properties of nonsingular solutions essentially expanded from previous one. Results on thermodynamics enlarged, their derivation simplified. Accepted for publication in Phys. Rev. D

References in corpus (1)

• Two-Dimensional Self-Consistent Quantum-Corrected Geometries with a Constant Dilaton Feld

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