analogue in four dimensions and its horizon has a spatial section diffeomorphic to $S^2\times S^1$. Thus, the uniqueness theorem is violated for rotating black holes. Recently, it has also been shown that a new family of black ring solutions violating the uniqueness appear when the system is coupled with form fields[@Emparan.R2004A], although the uniqueness holds for supersymmetric black holes in the five-dimensional minimal $N=1$ supergravity theory[@Reall.H2003]. Further, Emparan and Myers have pointed out that the Myers-Perry solutions in greater than five dimensions may suffer from a Gregory-Laflamme type instability for high angular momenta and argued that there may exist a new family of rotating solutions that bifurcates from the Myers-Perry family maintaining the symmetry. Such a symmetry preserving branch does not exist in five dimensions, as shown by Morisawa and Ida.

Along with these results in the asymptotically flat case, non-uniqueness has also been observed in Kaluza-Klein-type spacetimes. For example, Kudoh and Wiseman numerically constructed a family of non-uniform black string solutions in six dimensions. This family bifurcates from the uniform black string solution at the Gregory-Laflamme critical point. As discussed by Horowitz and Maeda, this family cannot be smoothly connected to a family of localised black hole solutions with 