  Recent work by Danielson, Satishchandran, and Wald (DSW) has shown that black
holes -- and, in fact, Killing horizons more generally -- impart a fundamental
rate of decoherence on all nearby quantum superpositions. The effect can be
understood from measurement and causality: An observer (Bob) in the black hole
should be able to disturb outside quantum superpositions by measuring their
superposed gravitational fields, but since his actions cannot (by causality)
have this effect, the superpositions must automatically disturb themselves. DSW
calculated the rate of decoherence up to an unknown numerical factor for
distant observers in Schwarzschild spacetime, Rindler observers in flat
spacetime, and static observers in de Sitter spacetime. Working in
electromagnetic and Klein-Gordon analogs, we flesh out and generalize their
calculation to derive a general formula for the precise decoherence rate for
Killing observers near bifurcate Killing horizons. We evaluate the rate in
closed form for an observer at an arbitrary location on the symmetry axis of a
Kerr black hole. This fixes the numerical factor in the distant-observer
Schwarzschild result, while allowing new exploration of near-horizon and/or
near-extremal behavior. In the electromagnetic case we find that the
decoherence vanishes entirely in the extremal limit, due to the "Black hole
Meissner effect" screening the Coulomb field from entering the black hole. This
supports the causality picture: Since Bob is unable to measure the field of the
outside superposition, no decoherence is necessary -- and indeed none occurs.
