One of the most impactful developments in science was the theoretical prediction of black holes in the context of the General Theory of Relativity. Each of these objects corresponds to a region of space-time delimited by a “membrane” called the horizon, where gravity is so strong that no form of matter/energy can escape from within it. This topic has a rich history that culminates in the first direct image of a black hole’s shadow taken in 2019.

In 1973, Kip Thorne formulated a statement known today as the Hoop Conjecture, which proposes to translate into the language of Physics the idea that a black hole arises if, and only if, a large amount of matter is compressed in a region whose size is small compared to its mass. As is usual in theoretical physics, General Relativity can be formulated through Mathematics. This project aims to find a precise mathematical formulation of the conjecture mentioned above and demonstrate it.