How to detect black holes via geometric inequalities?

Science / Mathematics

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.

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Chamada 6