Can it escape the event horizon if the wavelength is long enough?

[Puffer Fish]

TL;DR Summary

how very long wavelengths would interact with a black hole

Can electromagnetic radiation escape from the event horizon of a Black Hole if the wavelength is long enough?

What if a Black Hole contains electric charge, hypothetically supposing we dumped a large number of protons into it? Electric charge is mediated by the electromagnetic force. So the outside would not be able to feel any electric charge unless photons were able to permeate the boundary. (and we can say that the photons mediating static charges have extremely long wavelengths)

How can a photon with a wavelength longer than the diameter of the event horizon fit inside it?Some will claim "no energy can escape from a black hole", but here's one more thought experiment scenario to consider:
What if two black holes are circling each other very fast in a very tight orbit, one is positively charged and the other is negatively charged? You do not think that is going to be able to radiate electromagnetic energy? (it seems obvious to me it would. Hope that's not a false equivalency straw man though)

 

[PeterDonis]

Can electromagnetic radiation escape from the event horizon of a Black Hole if the wavelength is long enough?

No.

Electric charge is mediated by the electromagnetic force. So the outside would not be able to feel any electric charge unless photons were able to permeate the boundary.

Incorrect. If you are viewing the EM force as mediated by photons, they are virtual photons, which can, heuristically speaking, travel faster than light and so can get out of the hole.

However, General Relativity is a classical theory, not a quantum theory, so classical EM is really what you should be using in this scenario. And in classical EM, the static electric field of a charged black hole ultimately comes from charged matter in the past light cone of the observer who is measuring the field. In other words, the static electric field you feel if you are outside a charged black hole comes from whatever charged matter originally fell into the hole and gave it its charge. When that charged matter falls in, it leaves behind its static field, which continues to affect things outside.

(and we can say that the photons mediating static charges have extremely long wavelengths)

No, we can't. I have no idea where you are getting that from. In any case, as noted above, GR is a classical theory, not a quantum theory, so the correct EM theory to use here is classical EM, in which there are no "photons". If you want to discuss photons, you should open a new thread in the quantum physics forum.

How can a photon with a wavelength longer than the diameter of the event horizon fit inside it?

Again, in classical EM, there are no "photons". A classical EM wave with a wavelength longer than the size of a black hole will simply skip over the hole and won't go inside.

What if two black holes are circling each other very fast in a very tight orbit, one is positively charged and the other is negatively charged? You do not think that is going to be able to radiate electromagnetic energy?

If it does (it seems like it would, but AFAIK there is no known exact solution for this case), the radiation would be coming from outside the holes' horizons, generated by the non-static EM fields outside the holes' horizons; it would not be escaping from either hole.

 

[Janus]

Summary:: how very long wavelengths would interact with a black hole

Can electromagnetic radiation escape from the event horizon of a Black Hole if the wavelength is long enough?

no

What if a Black Hole contains electric charge, hypothetically supposing we dumped a large number of protons into it? Electric charge is mediated by the electromagnetic force. So the outside would not be able to feel any electric charge unless photons were able to permeate the boundary. (and we can say that the photons mediating static charges have extremely long wavelengths)

But the electromagnetic force is mediated by virtual photons, not actual photons. So no actual photons need to escape the event horizon.

Some will claim "no energy can escape from a black hole", but here's one more thought experiment scenario to consider:
What if two black holes are circling each other very fast in a very tight orbit, one is positively charged and the other is negatively charged? You do not think that is going to be able to radiate electromagnetic energy? (it seems obvious to me it would. Hope that's not a false equivalency straw man though)

Any electromagnetic energy produced would come at the expense of the orbital energy of the Black holes involved, causing them to spiral in on each other. ( the gravitational waves first detected were produced by such a process; Orbiting black holes emit gravitational waves, the energy of which is extracted from the orbital energy of the pair. They spiral in towards each other, and the faster orbit increases the wave ouput...)

 

[Heidi]

I think that something in a black hole cannot escape. But the scattering question of a particle with a black hole (it is the subject of the summary) is interesting. the probability of absorbtion doex not only depend on the energy of the particle. It also depends on the "surface" of the black hole and several other parameters.