Editing Cosmic censorship hypothesis (section)

==Example==
The [[Kerr metric]], corresponding to a black hole of mass <math>M</math> and angular momentum <math>J</math>, can be used to derive the [[effective potential]] for particle [[orbits]] restricted to the equator (as defined by rotation).  This potential looks like:<ref name="hartle_gravity">{{Cite book |last=Hartle |first=J. B. |title=Gravity: an introduction to Einstein's general relativity |date=2003 |publisher=[[Addison-Wesley]] |isbn=978-0-8053-8662-2 |location=San Francisco |chapter=15: Rotating Black Holes}}</ref>
<math display="block"> V_{\rm{eff}}(r,e,\ell)=-\frac{M}{r}+\frac{\ell^2-a^2(e^2-1)}{2r^2}-\frac{M(\ell-a e)^2}{r^3},~~~
a\equiv \frac{J}{M} </math>
where <math>r</math> is the coordinate radius, <math>e</math> and <math>\ell</math> are the test-particle's conserved energy and angular momentum respectively (constructed from the [[Killing vectors]]).

To preserve ''cosmic censorship'', the black hole is restricted to the case of <math>a < 1</math>.  For there to exist an [[event horizon]] around the singularity, the requirement <math>a < 1</math> must be satisfied.<ref name="hartle_gravity" />  This amounts to the [[angular momentum]] of the black hole being constrained to below a critical value, outside of which the horizon would disappear.  

The following thought experiment is reproduced from Hartle's ''Gravity'':

{{anchor|Violating cosmic censorship}}{{Block quote|Imagine specifically trying to violate the censorship conjecture.  This could be done by somehow imparting an angular momentum upon the black hole, making it exceed the critical value (assume it starts infinitesimally below it).  This could be done by sending a particle of angular momentum <math>\ell = 2Me</math>.  Because this particle has angular momentum, it can only be captured by the black hole if the maximum potential of the black hole is less than <math>(e^2-1)/2</math>.{{Break}}

Solving the above effective potential equation for the maximum under the given conditions results in a maximum potential of exactly <math>(e^2-1)/2</math>.  Testing other values shows that no particle with enough angular momentum to violate the censorship conjecture would be able to enter the black hole, ''because'' they have too much angular momentum to fall in.}}