On the stability of two-dimensional extremal black holes

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.