page_title: Naked singularity
section_title: Metrics
hierarchical_section_title: Naked singularity / Metrics
caption_attribution_description: English: Extremal Kerr-Newman black hole with spin a/M=√½ and charge Q/M=√½, in natural units of G=K=c=1. Therefore a²+Q²=M². The observer is at r=50M and views the black hole from the equatorial plane (edge on). FOV: 77.4°×38.7°. The equations that were used to raytrace the image can be found here.
context_page_description: In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon. In a black hole, the singularity is completely enclosed by a boundary known as the event horizon, inside which the gravitational force of the singularity is so strong that light cannot escape. Hence, objects inside the event horizon—including the singularity itself—cannot be directly observed. A naked singularity, by contrast, would be observable from the outside.
  The theoretical existence of naked singularities is important because their existence would mean that it would be possible to observe the collapse of an object to infinite density. It would also cause foundational problems for general relativity, because general relativity cannot make predictions about the future evolution of space-time near a singularity. In generic black holes, this is not a problem, as an outside viewer cannot observe the space-time within the event horizon.
  Naked singularities have not been observed in nature. Astronomical observations of black holes indicate that their rate of rotation falls below the threshold to produce a naked singularity.
context_section_description: 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 could 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 . However, this corresponds to a case where  exceeds  (or in Planck units, ), i.e. the spin exceeds what is normally viewed as the upper limit of its physically possible values.
  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 horizons 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. However, this corresponds to a case where  exceeds  (or in Planck units, ), i.e. the charge exceeds what is normally viewed as the upper limit of its physically possible values.
  See Kerr–Newman metric for a spinning, charged ring singularity.
caption: Comparison with an extremal black hole with M=1, a²+Q²=1M².
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