Single-rotating five-dimensional near-horizon extremal geometry in general relativity

The geometries with SL(2, R) and some axial U(1) isometries are called "near -horizon extremal geometries" and are found usually, but not necessarily, in the near -horizon limit of the extremal black holes. We present a new member of this family of solutions in five -dimensional Einstein -Hilbert gravity that has only one nonzero angular momentum. In contrast with the single -rotating Myers -Perry extremal black hole and its near -horizon geometry in five dimensions, this solution may have a nonvanishing and finite entropy. Although there is a uniqueness theorem that prohibits the existence of such single -rotating near -horizon geometries in five -dimensional general relativity, this solution has a curvature singularity at one of the poles, which breaks the smoothness conditions in the theorem.