In the toroidal Kaluza–Klein case, the existence of a toroidal action leads to further restrictions ; for instance, for and , each connected component of the horizon has necessarily one of the following topologies: , and .
It should be noted that no asymptotically-flat or Kaluza–Klein black holes with lens-space topology of the horizon are known. Constructing a black lens, or establishing non-existence, appears to be a challenging problem.
Living Rev. Relativity 15, (2012), 7
This work is licensed under a Creative Commons License.