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 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, 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 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.
By Penrose singularity theorem of 1964 it is known that if there is trapped null surface (and some other conditions) then a singularity must form, in 1983 Schoen and Yau proved how much matter must be crammed into a given volume to create a closed trapped surface,[1] sometimes referred as the Schoen-Yau black hole existence theorem[2] and more recently in 2023 using Gromov's "cube inequality"[3][2] some tori inequalities used in the results of 1983 have been generalized to cube ones which are more akin to Thorn's circular hoops.[4][2]
^Schoen, Richard; Yau, S. -T. (December 1983). "The existence of a black hole due to condensation of matter". Communications in Mathematical Physics. 90 (4): 575–579. Bibcode:1983CMaPh..90..575S. doi:10.1007/BF01216187. ISSN 0010-3616. S2CID 122331620.
^ abcNadis, Steve (16 August 2023). "Math Proof Draws New Boundaries Around Black Hole Formation". Quanta Magazine.
^Gromov, Misha (2019). "Four Lectures on Scalar Curvature". arXiv:1908.10612 [math.DG].
^Hirsch, Sven; Kazaras, Demetre; Khuri, Marcus; Zhang, Yiyue (2023). "Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem". arXiv:2301.08270 [math.DG].
The hoopconjecture, 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...
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on the basis of the strength of tests (notably straw-in-the-wind tests, hoop tests, smoking gun tests, double decisive tests). As a consequence, what...
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Shakespeare, and others. Of its authorship nothing certain is known. It is conjecture to associate it either with the name of Helinandus or with that of Petrus...
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swimmers. Scientific knowledge about sharks before 1916 was based on conjecture and speculation. The attacks forced ichthyologists to reassess common...
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titled "Observational Tests and Theoretical Problems Relating to the Conjecture That the Strength of the Electromagnetic Interaction May Be Variable"...
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interconnected relationship is the physiological explanation for the conjectured G-spot and experience of vaginal orgasms, taking into account the stimulation...
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on the board due to movement rules. Chess historian H. J. R. Murray conjectured that the ashtāpada was also used for some old race-type dice game, perhaps...
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