Supersymmetric Gödel and warped black holes in string theory
Geoffrey Compère, Stéphane Detournay, Mauricio Romo
TL;DR
The paper shows that Gödel black holes in three dimensions can be realized as exact string backgrounds via orbifolds of hyperbolic asymmetric deformations of the SL(2,R) WZW model, with a tachyonic string spectrum and a consistent uplift to Type II supergravity. It analyzes the supersymmetry properties, finding that extremal Gödel black holes preserve one Killing spinor in the 10D uplift, while non-extremal or certain extremal branches do not. The work connects these backgrounds to warped AdS3 geometries and discusses central charges, entropy via Cardy-like formulas, and the status of supersymmetry in related massive gravity theories, highlighting open questions about microscopic duals and brane realizations.
Abstract
It is observed that three-dimensional Gödel black holes can be promoted to exact string theory backgrounds through an orbifold of an hyperbolic asymmetric marginal deformation of the SL(2,R) WZW model. Tachyons are found in the spectrum of long strings. Uplifting these solutions in type IIB supergravity, extremal black holes are shown to preserve one supersymmetry in accordance with the BTZ limit. We also make connections with some recently discussed warped black hole solutions of topologically massive gravity, showing that they actually correspond to quotients of spacelike squashed AdS_3.