  It was previously shown that if an experimenter, Alice, puts a massive or
charged body in a quantum spatial superposition, then the presence of a black
hole (or more generally any Killing horizon) will eventually decohere the
superposition [arXiv:2205.06279, arXiv:2301.00026, arXiv:2311.11461]. This
decoherence was identified as resulting from the radiation of soft
photons/gravitons through the horizon, thus suggesting that the global
structure of the spacetime is essential for describing the decoherence. In this
paper, we show that the decoherence can alternatively be described in terms of
the local two-point function of the quantum field within Alice's lab, without
any direct reference to the horizon. From this point of view, the decoherence
of Alice's superposition in the presence of a black hole arises from the
extremely low frequency Hawking quanta present in Alice's lab. We explicitly
calculate the decoherence occurring in Schwarzschild spacetime in the Unruh
vacuum from the local viewpoint. We then use this viewpoint to elucidate (i)
the differences in decoherence effects that would occur in Schwarzschild
spacetime in the Boulware and Hartle-Hawking vacua; (ii) the difference in
decoherence effects that would occur in Minkowski spacetime filled with a
thermal bath as compared with Schwarzschild spacetime; (iii) the lack of
decoherence in the spacetime of a static star even though the vacuum state
outside the star is similar in many respects to the Boulware vacuum around a
black hole; and (iv) the requirements on the degrees of freedom of a material
body needed to produce a decoherence effect that mimics that of a black hole.
