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Starting with the two-derivative limit of $D=2$ string theory, we explore thespace of T-duality invariant $\alpha'$ corrections, a space that contains apoint representing the fully $\alpha'$-corrected classical string theory. Usinga parametrization introduced by Gasperini and Veneziano we obtain black holesolutions in this theory space. We prove that the dual of a solution with aregular horizon must have a curvature singularity. We find regions in thetheory space where the black hole is deformed while preserving the horizon andthe singularity, and regions where no black hole appears to exist. Furthermore,we find subregions in this theory space, probably not containing string theory,in which the black hole geometry exhibits a horizon leading to an interiorthat, having no singularity in the metric, curvature, or dilaton, is a regularcosmology.

On black hole singularity resolution in $D=2$ via duality-invariant $\alpha'$ corrections