kms 대한수학회

Black holes are perhaps the most celebrated predictions of general relativity. Miraculously, these complicated spacetimes arise as explicit (i.e., exact expression can be written down!) solutions to the vacuum Einstein equation. Looking these explicit black hole solutions leads to an intriguing observation: While the black hole exterior look qualitatively similar for every realistic black hole, the structure of the interior, in particular the nature of the `singularity' inside the black hole, changes drastically depending on whether the black hole is spinning (Kerr) or not (Schwarzschild).

A proposed picture for what happens in general is the so-called strong cosmic censorship conjecture of R. Penrose, which is a central conjecture in general relativity. In this colloquium, I will give a short introduction to general relativity and explain what this conjecture is. Time permitting, I will present some recent progress (joint work with J. Luk at Stanford) on related topics, using tools from nonlinear hyperbolic PDEs.