How can Black Holes generate EM fields ?

[Widdekind]

EM fields are mediated by virtual photons. And, photons cannot escape BHs. So, how can BHs generate EM fields ?

[swansont]

There are at least two effects you are ignoring: There was a time when those charged particles were not part of the black hole, and virtual photons do not behave like real photons, i.e. they do not propagate along the light cone.

[ajb]

If the black hole has an electric charge then it can act as a source of the electromagnetic field. The same question also arises if one wants to think about black holes as emitting gravitons.

 

Anyway, a charged black hole has a static electric field and this can penetrate through the horizon. The horizon does not allow any signals to be sent through, but a static field is time independent and thus does not convey any signals. So electrostatic fields are fine.

 

 

Now we want to think about photons being emitted from a black hole. The simple answer is that any time dependant fluctuations in the EM field must occur just on or outside the horizon. The same would be true of gravitational waves. This is all classical.

 

Quantum mechanically, as swansont has pointed out virtual photons are not constrained to move at a speed c or less. They can reach the "escape velocity" required.

[Widdekind]

If virtual photons can travel at supra-luminal speeds, then can EM interactions can be conveyed at such supra-luminal speeds? To wit, an electron "here" (Event 1), effects a proton "there" (Event 2), through space-like separations, in our space-time fabric ?

[ajb]

The first thing I would say when you do the calculations photon contributions to the amplitudes in QED get more and more suppressed the further the photons are off the light cone. So, in short the further off they are from "mass-shell" the less the contribute. This is for both faster and slower than the speed of light. When you add up all the momenta the contributions from "faster" and "slower" photons cancels. Remember this is all in the context of perturbation theory and virtual particles really appear as a convenient way to describe the mathematics of a formal series.

[Mystery111]

EM fields are mediated by virtual photons. And, photons cannot escape BHs. So, how can BHs generate EM fields ?

 

The fact light cannot escape from a black hole, has little bearing on the mathematics which dictates a black hole having a charge. A black hole can have a net charge, meaning the existence of an electric charge - if it rotates it will posses a magnetic charge. Static black holes in theory, do not contain magnetic charges. If one looks at the ''no hair'' theorem, you can see that all black holes will have atleast three properties, (or observables) those being mass, angular momentum and charge. It has been shown however, that all black holes will have a poloidal and toroidal magnetic field, so this adds a new observable to a rotating black hole.

[questionposter]

Anyway, a charged black hole has a static electric field and this can penetrate through the horizon. The horizon does not allow any signals to be sent through, but a static field is time independent and thus does not convey any signals. So electrostatic fields are fine.

 

Wait, so the electromagnetic force actually travels from the singularity of a black hole past the event horizon? Couldn't signals be sent in the form of pulses? Also, doesn't that mean that whatever the force carrier is for the EM force isn't effected by the distortion of the fabric of space which means you should be able to measure some property of it as a constant?

Edited August 30, 2011 by questionposter

[questionposter]

Really? No one?

Ok well how about just the first thing then, where the EM force can travel from the singularity to past the event horizon?

[ajb]

Wait, so the electromagnetic force actually travels from the singularity of a black hole past the event horizon? Couldn't signals be sent in the form of pulses?

 

Electrostatic fields can. This is also a consequence of general relativity being a local theory, if you know the fields before the gravitational collapse then you known them after.

 

Signals are not static fields and so are excluded from what I said.

[MigL]

So time varying fields are not allowed while static fields can be considered to 'pass through' the event horizon. Or would it better to consider the field as originating at the event horizon since the horizon preserves pre-collapse static field information.

In effect, what is the difference and consequence of considering the mass and charge of a black hole to be localised either at the 'centre' of the event horizon, or the 'surface' of the event horizon ?

[Widdekind]

Are EM-force-carrying virtual photons red-shifted, by the distortions of the space-time fabric, near compact objects ?