The Shape of a Black Hole

Black holes are already strange enough, regions of space where gravity is so extreme that not even light can escape. But physicists have long known there's another layer of weirdness, that black holes also behave like thermodynamic objects, with temperature, entropy, and phase transitions just like a gas or a liquid. Now, a new approach borrowed from pure mathematics is revealing hidden patterns in that behaviour and hinting at something fundamental about the nature of black holes themselves.