Decoherence near extremal black holes: Meissner protection depends on where the superposition is held

A static spatial superposition outside a Killing horizon decoheres at a constant rate. Near extremality this rate is known to vanish for sources held at fixed radius, for the electromagnetic field because the horizon expels the field (black-hole Meissner effect). We show that near extremality the relevant scale is the local temperature, not the Hawking temperature, so that the protection depends on where the superposition is held. Inside the near-horizon throat of a near-extremal Reissner–Nordström black hole, at fixed proper distance from the horizon, the rate per unit proper time of the lab stays finite for both scalar and electromagnetic fields, and the horizon charge is not expelled; per unit Killing time it vanishes. The same holds on the axis of near-extremal Kerr with M → √2 M; off the axis, for co-rotating sources, the local-temperature law fails. These follow from closed-form rates at arbitrary radius and charge, summed over all multipoles. The throat rates are the Rindler rates with the acceleration replaced by 2πT_loc, the local Tolman temperature; the same law holds at every point of the de Sitter static patch for scalar, electromagnetic and gravitational couplings, fixes the Rindler graviton coefficient, and fails in the static exterior away from the throat. For the scalar field it requires that the proper time of each branch be kept. A held source localized within the throat carries more energy than the Schwarzian breakdown scale; if this energy counts toward the energy above extremality, as in JT gravity, the semiclassical throat results are self-consistent. The accompanying zip contains the LaTeX source and the Python scripts that reproduce all results (run_all.py).