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Say we have a Reissner-Nordström charged black hole. There is a static electric field around it and far away it is that of a point charge. This poses a puzzle because signals cannot travel outside a black hole. According to this Phys.SE answer and the link contained therein,

  • Classically we may say the Coulomb potential is sourced by infalling charged particles in the far past light cone of a test particle.

  • Quantum mechanically the Coulomb potential comes from mediating virtual photons sourced by the infalling charged particles in the far past and the black hole itself. That is, according to the second link, virtual photons can cross a black hole event horizon.

1) Is this true? ("...the electromagnetic interaction between a test charge and the black hole is mediated by both horizon-crossing and non-horizon-crossing virtual photons.")

2) What can't virtual photons do? Doesn't that violate causality? I know that virtual photons, in flat spacetime QFT, do not violate causality because we don't need to assume they exist; they can be considered a mathematical device requiring no physical interpretation. But causality bans interaction between a test particle and the inside of a black hole.

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This link (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html) offers a good answer. In particular,

1) Yes, it is true

2) There is really no difference between a virtual photon traveling violating locality in flat QFT and a virtual photon going outside a black hole. Both are instances of escaping its light cone.

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