Exactly solvable models in 2D semiclassical dilaton gravity and extremal black holes

TL;DR

This paper explores special cases of 2D semiclassical dilaton gravity models that admit extremal black holes, analyzing their properties, quantum effects, and conditions for their existence and stability.

Contribution

It identifies degenerate cases of exactly solvable models that include extremal black holes and extends previous models to incorporate electric charge under specific conditions.

Findings

Existence of degenerate models with extremal black holes

Quantum backreaction prevents ultraextremal black holes

Conditions for eliminating divergencies in quantum stresses

Abstract

Previously known exactly solvable models of 2D semiclassical dilaton gravity admit, in the general case, only non-extreme black holes. It is shown that there exist exceptional degenerate cases, that can be obtained by some limiting transitions from the general exact solution, which include, in particular, extremal and ultraextremal black holes. We also analyze properties of extreme black holes without demanding exact solvability and show that for such solutions quantum backreaction forbids the existence of ultraextreme black holes. The conditions,under which divergencies of quantum stresses in a free falling frame can disappear, are found. We derive the closed equation with respect to the metric as a function of the dilaton field that enables one, choosing the form of the metric, to restore corresponding Lagrangian. It is demonstrated that exactly solvable models, found earlier, can be extended to include an electric charge only in two cases: either the dilaton-gravitation coupling is proportional to the potential term, or the latter vanishes. The second case leads to the effective potential with a negative amplitude and we analyze, how this fact affects the structure of spacetime. We also discuss the role of quantum backreaction in the relationship between extremal horizons and the branch of solutions with a constant dilaton.