Existence and uniqueness of near-horizon geometries for 5-dimensional black holes

We prove existence of all possible bi-axisymmetric near-horizon geometries of 5-dimensional minimal supergravity. These solutions possess the cross-sectional horizon topology S 3 , S 1 × S 2 , or L ( p , q ) and come with prescribed electric charge, two angular momenta, and a dipole charge (in the ring case). Moreover, we establish uniqueness of these solutions up to an isometry of the symmetric space G 2 ( 2 ) ∕ S O ( 4 ) .