Dilatonic black holes in higher curvature string gravity. II. Linear stability

We demonstrate the linear stability of dilatonic black holes appearing in a string-inspired higher-derivative gravity theory with a Gauss-Bonnet curvature-squared term. The proof is accomplished by mapping the system to a one-dimensional Schr\"odinger problem which admits no bound states. This result is important in that it constitutes a linearly stable example of a black hole that bypasses the ``no-hair conjecture.'' However, dilaton hair is secondary in the sense that it is not accompanied by any new quantum number for the black hole solution.