The classical stability of charged (1 + 1)-dimensional black holes

Abstract

We discuss the classical stability of charged, two-dimensional, black holes. Here is the dilaton - Maxwell coupling parameter. We introduce a tachyon field, which arises from string theories, as a test field. One finds barrier - well type potentials surrounding the extremal black holes, which induce the classical instability. For the non-extremal black holes, one finds the barrier - well type potentials between the inner (Cauchy) horizon and outer (event) horizon, while potential barriers appear outside the event horizon. This implies that the inner horizons are unstable and the outer horizons are stable. However, this means that the non-extremal black holes themselves are stable because the stability of a black hole depends only on the outer horizon. Finally we mention that the instability of extremal black holes may originate from the unstable inner horizon of non-extremal black holes.