We study the first-order ${\alpha }^{\prime }$ corrections to the singular four-dimensional massless stringy black holes studied in the 1990s in the context of the heterotic superstring. We show that the ${\alpha }^{\prime }$ corrections not only induce a nonvanishing mass and give rise to an event horizon but also eliminate the singularity, giving rise to a regular spacetime whose global structure includes further asymptotically flat regions in which the mass of the spacetime is positive or negative. We study the timelike and null geodesics and their effective potential, showing that the spacetime is geodesically complete. We discuss the validity of this solution, arguing that the very interesting and peculiar properties of the solution are associated to the negative energy contributions coming from the terms quadratic in the curvature. As a matter of fact, the ten-dimensional configuration is singular. We extract some general lessons on attempts to eliminate black-hole singularities by introducing terms of higher order in the curvature.

• Received 13 July 2018

DOI:https://doi.org/10.1103/PhysRevD.99.046014

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Published by the American Physical Society