Helliwell-Konkowski Conjecture and the Singularities of CauchyHorizons in 1 + 1-Dimensional Black Holes

The stability conjecture of Cauchy horizons of black holes suggested by Helliwell and Konkowski is used to investigate the 1+1-dimensional (2D) black holes under perturbations of infalling null dust and of both infalling and outgoing null dust. The result given by this conjecture agrees with that from mass inflation scenario for 2D charged dilaton black hole. For 2D black holes, we show that the Cauchy horizons are unstable and the corresponding singularities exist.