Metrics
Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum. Specifically, if the angular momentum is high enough the event horizons will disappear. Transforming the Kerr metric to Boyer-Lindquist coordinates, it can be shown that the coordinate (which is not the radius) of the event horizon is
,
where, and . In this case, "event horizons disappear" means when the solutions are complex for, or .
Disappearing event horizons can also be seen with the Reissner-Nordström geometry of a charged black hole. In this metric it can be shown that the singularities occur at
,
where, and . Of the three possible cases for the relative values of and, the case where causes both to be complex. This means the metric is regular for all positive values of, or in other words the singularity has no event horizon.
See Kerr-Newman metric for a spinning, charged ring singularity.
Read more about this topic: Naked Singularity