Two-dimensional extremal black holes

We discuss the two-dimensional (2D), $\epsilon<2$ extremal ground states of charged black hole. Here $\epsilon$ is the dilaton coupling parameter for the Maxwell term. The complete analysis of stability is carried out for all these extremal black holes. It is found that they are all unstable. To understand this instability, we study the non-extremal charged black hole with two (inner and outer) horizons. The extremal black holes appear when two horizons coalesce. It conjectures that the instability originates from the inner horizon.