On Attractor Flow and Small Black Holes

We study the attractor flow and near horizon geometry of two-charge small black holes in heterotic string theory. The Hessian of Sen’s entropy function with respect to the moduli fields has standard attractor properties and shows the interesting factorization at the attractor fixed points. We notice that the stability conditions are preserved under arbitrary ${\alpha }^{\mathrm{\prime }}$-corrections to the black hole solutions.