Black holes with spindles at the horizon

Abstract: We construct $AdS_4 \times \Sigma$ and $AdS_2 \times \Sigma \times \Sigma_g$ solutions in F(4) gauged supergravity in six dimensions, where $\Sigma$ is a two dimensional manifold of non-constant curvature with conical singularities at its two poles, called a spindle, and $\Sigma_g$ is a constant curvature Riemann surface of genus g. We find that the first solution realizes a "topologically topological twist", while the second class of solutions gives rise to an "anti twist". We compute the holographic free energy of the $AdS_4 \times \Sigma$ solution and find that it matches the entropy computed by extremizing an entropy functional that is constructed by gluing gravitational blocks. For the $AdS_2 \times \Sigma \times \Sigma_g$ solution, we find that the Bekenstein-Hawking entropy is reproduced by extremizing an appropriately defined entropy functional, which leads us to conjecture that this solution is dual to a three dimensional SCFT on a spindle. A class of the $AdS_2 \times \Sigma \times \Sigma_g$ solutions can be embedded in four dimensional T3 gauged supergravity, which is a subtruncation of the six dimensional theory.