The black body spectrum of a black hole

Stephen Hawking developed the definition of a classical black hole as a region of spacetime from which nothing gets out. He then famously turned this upside down, and introduced a cornerstone of quantum gravity, by computing that black holes radiate quantum mechanical particles. This discussion will highlight where the black hole geometry comes in at key steps to give the result that the radiation spectrum is a black body, with temperature proportional to the surface gravity (a geometrical property) of the black hole.