Lecture 15: Hawking Radiation Through Ray-Tracing
In this lecture, we reviewed Hawking's original derivation of the Hawking radiation formula through ray-tracing. The main geometric insight that goes into this derivation is the behaviour of geodesics in the collapsing black hole-geometry. Light rays that embark from past null-infinity after a "last ray" get stuck inside the black hole. Light rays that embark from past null-infinity just before the "last ray" emerge to future null infinity. But an infinite region (in affine-parameter space) on future null infinity is generated by a very small region just before the last-ray on past-null infinity.
By working out the quantitative formula that relates the starting position of geodesics on past null-infinity with their final position on future null infinity we were able to work out the Bogoliubov coefficients between waves with support on future null infinity and waves with support on past null infinity. This led to the derivation of the Hawking radiation formula.
