Curvature-corrected dilatonic black holes and black hole – string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss–Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling $g_s$, the situation can tentatively be interpreted as classical indication on the black hole – string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss–Bonnet gravity. Here we work in the string frame version of the theory with the $S$-duality symmetric dilaton function as required by the heterotic string theory.