Topological transitions and enhançon‐like geometries in Calabi‐Yau compactifications of M‐theory

We study the impact of topological phase transitions of the internal Calabi‐Yau threefold on the space‐time geometry of five‐dimensional extremal black holes and black strings. For flop transitions and SU (2) gauge symmetry enhancement we show that solutions can always be continued and that the behaviour of metric, gauge fields and scalars can be characterized in a model independent way. Then we look at supersymmetric solutions which describe naked singularities rather than geometries with a horizon. For black strings we show that the solution cannot become singular as long as the scalar fields take values inside the Kähler cone. For black holes we establish the same result for the elliptic fibrations over the Hirzebruch surfaces ℱ 0 , ℱ 1 , ℱ 2 . These three models exhibit a behaviour similar to the enhançon, since one runs into SU (2) enhancement before reaching the apparent singularity. Using the proper continuation inside the enhançon radius one finds that the solution is regular.