Unstable two-dimensional extremal black holes

TL;DR

This paper investigates the stability of new extremal charged black hole solutions in two-dimensional gravity with dilaton coupling, finding they are unstable and thus unsuitable as models for stable black hole endpoints.

Contribution

It introduces new extremal black hole ground states for $\, ext{epsilon}<2$ in 2D gravity and analyzes their stability, revealing their inherent instability.

Findings

All these extremal black holes are unstable due to potential barrier-well structures.

The shape of the potentials indicates the presence of bound states implying instability.

These black holes should not be used as stable models for Hawking evaporation endpoints.

Abstract

We obtain the $\epsilon<2$ new extremal ground states of a two-dimensional (2D) charged black hole where $\epsilon$ is the dilaton coupling parameter for the Maxwell term. The stability analysis is carried out for all these extremal black holes. It is found that the shape of potentials to an on-coming tachyon (as a spectator) take all barrier-well types. These provide the bound state solutions, which imply that they are unstable. We conclude that the 2D, $\epsilon<2$ extremal black holes should not be considered as a toy model for the stable endpoint of the Hawking evaporation.