Hoop Conjecture
Encyclopedia
The Hoop Conjecture, proposed by Kip Thorne
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. The critical circumference is given by:
where:
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
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.
Kip Thorne
Kip Stephen Thorne is an American theoretical physicist, known for his prolific contributions in gravitation physics and astrophysics and for having trained a generation of scientists...
in 1972, states that an imploding object forms a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
when, and only when, a circular hoop with a specific critical circumference could be placed around the object and rotated. The critical circumference is given by:
where:
-
is the critical circumference; -
is the object's Schwarzschild radiusSchwarzschild radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
;
Thorne calculated the effects of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
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
Event horizon
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
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.