Question

There is well known gravitational redshift of real photons. What about gravitational redshift of virtual photons of charged neutron star? Is electrostatic force become weaker while mass of charged neutron star is growing?

How can electrostatic field of a charged particle swallowed by a black hole escape from the event horizon? How can charged black holes exist at all?

Answer 1

There is a difference between the value of a field, and the excitations of that field. If you have a speherically symmetric charge distribution collapse to a black hole (while maintaining the spherical symmetry), there is no electric nor gravitational radiation--Gauss's Law and Birkhoff's Theorem work in tandem to keep the gravitational and electric forces constant far from the object, and since there is nothing to propogate, nothing needs to propogate. The field already lives out in the place where information about where the charge distribution needs to go.

What is a photon, then? A photon is a propogating disturbance in the electromagnetic field. You need to have an accelerating charge in order to produce such a disturbance, and there's no need to violate causality at the black hole horizon in order for a particle to feel force from a field that already exists locally--if, say, an electron were coming close to a charged black hole, it would see the field that existed there, scatter off of the field, and emit a photon. (and of course, it's new field would be set up and propogate to the black hole, and scatter the black hole--but there's no problem with information falling IN to a black hole, which is allowed to externally display it's mass, charge, angular momentum and linear momentum, all of which get inprinted on the horizon as matter falls in).

So, in summary, it's not necessary for a photon to be emitted in order for a second particle to feel a force--electrostatic forces in fact don't involve photons at all (at least, until the scattering event begins).