Global geometry of two-dimensional charged black holes

TL;DR

This paper investigates the semiclassical geometry of two-dimensional charged black holes, revealing how pair-creation effects influence singularity structure, stability, and the nature of extremal solutions, with numerical analysis showing critical behavior at formation thresholds.

Contribution

It introduces a systematic way to include pair-creation effects in 2D charged black hole models, showing how these effects alter classical features like singularities and stability.

Findings

Classical mass-inflation instability is amplified by quantum effects.

Semiclassical solutions have spacelike singularities similar to neutral black holes.

Extremal black holes are destabilized by pair-creation, leading to non-extremal geometries.

Abstract

The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation.