Near-extremal and extremal quantum-corrected two-dimensional charged black holes

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 Mtot < Q (Q is a charge). We show that in the limit TH → 0 (where TH is the Hawking temperature) the mass and geometry of the 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 κ would be) of a non-extremal configuration does not tend to the quantum-corrected extremal one but to the special branch of solutions with the constant dilaton (2D analogue of the Bertotti–Robinson metric) instead. Meanwhile, if κ = 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 the 4D case and show that for the quantum-corrected extremal black hole Mtot > Q.