the electron falls and emits radiation. will it lose all it's energy by the time it reaches the event horizon or will it have enough (>2m) to produce a particle shower? Will other things happen?
I just learned about the quantization of the em field. Then EM field 4-potential has components A^mu, giving you 4 degrees of freedom. That gets reduced to 2 degrees of freedom (2 polarization states), that gets done to impose the Lorenz gauge onto free photons. SO what the hell happens to the...