De-singularizing the extremal GMGHS black hole via higher derivatives corrections

Abstract: The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is an influential solution of the low energy heterotic string theory. As it is well known, it presents a singular extremal limit. We construct a regular extension of the GMGHS extremal black hole in a model with $\mathcal{O}(\alpha')$ corrections in the action, by solving the fully non-linear equations of motion. The de-singularization is supported by the $\mathcal{O}(\alpha')$-terms. The regularised extremal GMGHS BHs are asymptotically flat, possess a regular (non-zero size) horizon of spherical topology, with an $AdS_2\times S^2$ near horizon geometry, and their entropy is proportional to the electric charge. The near horizon solution is obtained analytically and some illustrative bulk solutions are constructed numerically.