Instability of a two-dimensional extremal black hole

TL;DR

This paper demonstrates that a two-dimensional extremal electrically charged black hole is classically unstable due to tachyonic perturbations, challenging its viability as a stable endpoint of Hawking evaporation.

Contribution

It provides a detailed analysis of tachyon perturbations showing the classical instability of 2D extremal black holes, a novel insight into their stability properties.

Findings

Presence of a double-humped potential barrier for tachyon waves

Existence of exponentially growing modes indicating instability

Conclusion that extremal black holes cannot be stable endpoints of evaporation

Abstract

We consider the perturbation of tachyon about the extremal ground state of a two-dimensional (2D) electrically charged black hole. It is found that the presenting potential to on-coming tachyonic wave takes a double-humped barrier well. This allows an exponentially growing mode with respect to time. This extremal ground state is classically unstable. We conclude that the 2D extremal electrically charged black hole cannot be a candidate for the stable endpoint of the Hawking evaporation.