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

TL;DR

This paper investigates how $ ext{D}=2$ string theory's black hole solutions are affected by duality-invariant $ ext{α'}$ corrections, revealing conditions under which singularities are resolved or replaced by regular cosmologies.

Contribution

It introduces a parametrization of $ ext{α'}$ corrections in $ ext{D}=2$ string theory and analyzes the resulting black hole solutions, identifying regions with regular horizons and singularities.

Findings

Dual solutions with regular horizons necessarily have curvature singularities.

Certain regions in theory space allow black holes with regular, non-singular interiors.

Some theory regions produce horizonless, regular cosmological solutions.

Abstract

Starting with the two-derivative limit of $D=2$ string theory, we explore the space of T-duality invariant $\alpha'$ corrections, a space that contains a point representing the fully $\alpha'$-corrected classical string theory. Using a parametrization introduced by Gasperini and Veneziano we obtain black hole solutions in this theory space. We prove that the dual of a solution with a regular horizon must have a curvature singularity. We find regions in the theory space where the black hole is deformed while preserving the horizon and the 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 interior that, having no singularity in the metric, curvature, or dilaton, is a regular cosmology.