Light Ring Topological Theorems in Strong Gravity

Explore a physics lecture examining theorems about light rings and their topological charges, focusing on stationary and axisymmetric ultracompact objects. Delve into the mathematical proof that objects forming from smooth, quasi-Minkowski physical initial data must contain at least one stable light ring, which can trigger spacetime instability. Study ultracompact bosonic stars as test cases to verify these instabilities, discovering their eventual fate of either migrating to non-ultracompact configurations or collapsing into black holes. Learn how these findings support the theory that light ring instability effectively eliminates horizonless ultracompact objects that could potentially mimic black holes.