The hoop conjecture, proposed by
Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. F ...
in 1972, states that an
imploding object forms a
black hole when, and only when, a circular hoop with a specific critical circumference could be placed around the object and rotated about its diameter. In simpler terms, the entirety of the object's mass must be compressed to the point that it resides in a perfect sphere whose radius is equal to that object's
Schwarzschild radius
The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteris ...
, if this requirement is not met, then a black hole will not be formed. The critical circumference required for the imaginary hoop is given by the following equation listed below.
:
where
:
is the critical circumference;
:
is the object's Schwarzschild radius;
Thorne calculated the effects of
gravitation on objects of different shapes (spheres, and cylinders that are infinite in one direction), and concluded that the object needed to be compressed in all three directions before gravity led to the formation of a black hole. With cylinders, the
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.
In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact ob ...
was formed when the object could fit inside the hoop described above. The mathematics to prove the same for objects of all shapes was too difficult for him at that time, but he formulated his hypothesis as the hoop conjecture.
See also
*
General relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
*
Bounding sphere
In mathematics, given a non-empty set of objects of finite extension in d-dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is an d-dimensional solid sphere containing all of the ...
References
*
Thorne, Kip, ''
Black Holes and Time Warps: Einstein's Outrageous Legacy'', W. W. Norton & Company; Reprint edition, January 1, 1995. .
General relativity
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