Spindle black holes in AdS${}_4\times$SE${}_7$

We construct new classes of supersymmetric AdS${}_2\times \mathrm{\Sigma }$ solutions of 4d gauged supergravity in presence of charged hypermultiplet scalars, with $\mathrm{\Sigma }$ the complex weighted projective space known as a spindle. These solutions can be viewed as near-horizon geometries of asymptotically Anti de-Sitter (AdS${}_4$) black holes with magnetic fluxes that admit embedding in 11d on Sasaki-Einstein (SE${}_7$) manifolds, which renders them of holographic interest. We show that in each case the Bekenstein-Hawking entropy follows from the procedure of gluing two gravitational blocks, ultimately determined by SE${}_7$ data. This allows us to establish the general form of the gravitational blocks in gauged 4d $\mathcal{N}=2$ supergravity with charged scalars and massive vectors. Holographically, our results provide a large N answer for the spindle index with anti-twist and additional mesonic or baryonic fluxes of a number of $\mathcal{N}=2$ Chern-Simons-matter theories.