O.B. Zaslavskii
Near-Extremal and Extremal Quantum-Corrected Two-Dimensional Charged Black Holes
Preprint series: ESI preprints

MSC:

83C57 Black holes

83E15 Kaluza-Klein and other higher-dimensional theories

PACS: 04.70.Dy,04.60.Kz
Abstract: We consider charged black holes within dilaton gravity with
exponential-linear dependence of action coefficients on dilaton and minimal
coupling to quantum scalar fields. This includes, in particular, CGHS and
RST black holes in the uncharged limit. For non-extremal configuration
quantum correction to the total mass, Hawking temperature, electric
potential and metric are found explicitly and shown to obey the first
generalized law. We also demonstrate that quantum-corrected extremal black
holes in these theories do exist and correspond to the classically forbidden
region of parameters in the sense that the total mass $M_{tot}charge). We show that in the limit $T_{H}\rightarrow 0$ (where $T_{H}$ is
the Hawking temperature) the mass and geometry of non-extremal configuration
go smoothly to those of the extremal one, except from the narrow
near-horizon region. In the vicinity of the horizon the quantum-corrected
geometry (however small quantum the coupling parameter $\kappa $ would be)
of a non-extremal configuration tends to not the quantum-corrected extremal
one but to the special branch of solutions with the constant dilaton (2D
analog of the Bertotti-Robinson metric) instead. Meanwhile, if $\kappa =0$
exactly, the near-extremal configuration tends to the extremal one. We also
consider the dilaton theory which corresponds classically to the
spherically-symmetrical reduction from 4D case and show that for the
quantum-corrected extremal black hole $M_{tot}>Q$.