Singularity Theorems Proven in Non-Smooth Spacetimes

Mathematicians have long sought to prove singularity theorems in general relativity, such as Hawking's singularity theorem, but these theorems rely on the assumption of smooth spacetime. Recently, researchers cleverly used a 'triangle comparison method' and 'optimal transport theory' to prove special cases of these singularity theorems in non-smooth spacetimes, even extending to more general spacetime models. This breakthrough not only strengthens the mathematical foundation of the Big Bang singularity theory but also provides new mathematical tools for quantum gravity research, paving the way for unifying general relativity and quantum physics.