Three-dimensional black holes from deformed anti-de Sitter

TL;DR

This work constructs exact three-dimensional string backgrounds by exploring marginal current-current deformations of the SL$(2,\mathbb{R})$ WZW model and applying discrete identifications. It develops both symmetric (gravitational) and asymmetric (electromagnetic) deformations, including a two-parameter double deformation that yields NS–NS flux and an electric field, and analyzes their global structure, horizons, and potential naked singularities. The authors provide a unified CFT description with explicit expressions for the deformed spectra, using $O(2,2)$ transformations on charge lattices and parafermion decompositions, and extend the construction to twisted sectors via orbifolding. These results advance exact string-background realizations of BTZ-like black holes and three-dimensional black strings, offering precise links between worldsheet marginal deformations and spacetime geometry with potential holographic implications.

Abstract

We present new exact three-dimensional black-string backgrounds, which contain both NS--NS and electromagnetic fields, and generalize the BTZ black holes and the black string studied by Horne and Horowitz. They are obtained as deformations of the Sl(2,R) WZW model. Black holes resulting from purely continuous deformations possess true curvature singularities. When discrete identifications are introduced, extra chronological singularities appear, which under certain circumstances turn out to be naked. The backgrounds at hand appear in the moduli space of the Sl(2,R) WZW model. Hence, they provide exact string backgrounds and allow for a more algebraical CFT description. This makes possible the determination of the spectrum of primaries.