Editing Gravitational singularity (section)

===Naked singularity===
{{Main Article|Naked singularity}}
Until the early 1990s, it was widely believed that general relativity hides every singularity behind an [[event horizon]], making naked singularities impossible. This is referred to as the [[cosmic censorship hypothesis]]. However, in 1991, physicists Stuart Shapiro and [[Saul Teukolsky]] performed computer simulations of a rotating plane of dust that indicated that general relativity might allow for "naked" singularities. What these objects would actually look like in such a model is unknown. Nor is it known whether singularities would still arise if the simplifying assumptions used to make the simulation were removed. However, it is hypothesized that light entering a singularity would similarly have its geodesics terminated, thus making the [[naked singularity]] look like a black hole.<ref>{{Cite journal |last=Bojowald |first=Martin |year=2008 |title=Loop Quantum Cosmology |journal=Living Reviews in Relativity |language=en |volume=11 |issue=1 |pages=4 |bibcode=2008LRR....11....4B |doi=10.12942/lrr-2008-4 |issn=2367-3613 |pmc=5255532 |pmid=28163606 |doi-access=free}}</ref><ref>{{Cite journal |last1=Goswami |first1=Rituparno |last2=Joshi |first2=Pankaj S. |year=2008 |title=Spherical gravitational collapse in N dimensions |journal=Physical Review D |language=en |volume=76 |issue=8 |pages=084026 |arxiv=gr-qc/0608136 |bibcode=2007PhRvD..76h4026G |doi=10.1103/PhysRevD.76.084026 |issn=1550-7998 |s2cid=119441682}}</ref><ref>{{Cite journal |last1=Goswami |first1=Rituparno |last2=Joshi |first2=Pankaj S. |last3=Singh |first3=Parampreet |date=2006-01-27 |title=Quantum Evaporation of a Naked Singularity |journal=Physical Review Letters |language=en |volume=96 |issue=3 |pages=031302 |arxiv=gr-qc/0506129 |bibcode=2006PhRvL..96c1302G |doi=10.1103/PhysRevLett.96.031302 |issn=0031-9007 |pmid=16486681 |s2cid=19851285}}</ref>

Disappearing event horizons exist in the&nbsp;[[Kerr metric]], which is a spinning black hole in a vacuum, if the&nbsp;[[angular momentum]]&nbsp;(<math>J</math>) is high enough. Transforming the Kerr metric to&nbsp;[[Boyer–Lindquist coordinates]], it can be shown<ref>{{harvnb|Hobson|Efstathiou|Lasenby|2013|pp=300-305}}.</ref>&nbsp;that the coordinate (which is not the radius) of the event horizon is, <math>r_{\pm} = \mu \pm \left(\mu^{2} - a^{2}\right)^{1/2}</math>, where&nbsp;<math>\mu = G M / c^{2}</math>, and&nbsp;<math>a=J/M c</math>. In this case, "event horizons disappear" means when the solutions are complex for&nbsp;<math>r_{\pm}</math>, or&nbsp;<math>\mu^{2} < a^{2}</math>. However, this corresponds to a case where <math>J</math> exceeds <math>GM^{2}/c</math> (or in [[Planck units]], {{Nowrap|<math>J > M^{2}</math>)}}; i.e. the spin exceeds what is normally viewed as the upper limit of its physically possible values.

Similarly, disappearing event horizons can also be seen with the&nbsp;[[Reissner–Nordström metric|Reissner–Nordström]]&nbsp;geometry of a charged black hole if the charge&nbsp;(<math>Q</math>) is high enough. In this metric, it can be shown<ref>{{harvnb|Hobson|Efstathiou|Lasenby|2013|pp=320-325}}.</ref>&nbsp;that the singularities occur at <math>r_{\pm}= \mu \pm \left(\mu^{2} - q^{2}\right)^{1/2}</math>, where&nbsp;<math>\mu = G M / c^{2}</math>, and&nbsp;<math>q^2 = G Q^2/\left(4 \pi \epsilon_0 c^4\right)</math>. Of the three possible cases for the relative values of&nbsp;<math>\mu</math> and&nbsp;<math>q</math>, the case where&nbsp;<math>\mu^{2} < q^{2}</math>&nbsp;causes both&nbsp;<math>r_{\pm}</math> to be complex. This means the metric is regular for all positive values of&nbsp;<math>r</math>, or in other words, the singularity has no event horizon. However, this corresponds to a case where <math>Q/\sqrt{4 \pi \epsilon_0}</math> exceeds <math>M\sqrt{G}</math> (or in Planck units, {{Nowrap|<math>Q > M</math>)}}; i.e. the charge exceeds what is normally viewed as the upper limit of its physically possible values. Also, actual astrophysical black holes are not expected to possess any appreciable charge.

A black hole possessing the lowest <math>M</math> value consistent with its <math>J</math> and <math>Q</math> values and the limits noted above; i.e., one just at the point of losing its event horizon, is termed [[extremal black hole|extremal]].