On the stability of two-dimensional extremal black holes

TL;DR

This paper investigates the classical stability of two-dimensional extremal charged black holes, finding they are unstable due to bound state solutions that lead to exponential growth over time.

Contribution

It introduces a method to analyze stability by deriving a Schrödinger-like equation and demonstrates the instability of 2D extremal black holes.

Findings

Potential forms a barrier-well type for incoming tachyons

Bound state solutions imply exponential growth modes

All extremal ground states are classically unstable

Abstract

We discuss the stability of the extremal ground states of a two-dimensional (2D) charged black hole which carries both electric ($Q_E$) and magnetic ($Q_M$) charges. The method is first to find the physical field and then to derive the equation of the Schr\"odinger type. It is found that the presenting potential to an on-coming tachyon (as a spectator) takes a barrier-well type. This provides the bound state solution, which implies an exponentially growing mode with respect to time. The 2D extremal ground states all are classically unstable. We conclude that the 2D extremal charged black holes are not considered as the candidates for the stable endpoint of the Hawking evaporation.