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

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?

The hole itself will then have an electric charge. The entire hole. No need for photons to escape from within the hole. No way for them to do so in fact.

No. No energy can escape from a black hole.

Same way your car antenna, which is only a few millimeters in width, can receive a radio-wave photon with a wavelength of thirty meters or so. The wavelength isn’t really a “physical thing.” You can’t go imagining thirty meters of clothesline, vibrating like a string. The quantum equations describe the spread-out nature of photons.

It’s all in the math.

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?

For what it’s worth, Hawking radiation consists mostly of wavelengths comparable to the size of the hole, and it’s not entirely wrong to think of it as light escaping in this way. For a hole of reasonable size, though, it’s incredibly slow.

EDIT: Yes, two charged holes orbiting each other will radiate significant electromagnetic energy. That energy comes from the orbital energy, though, not from the holes themselves.

I fully understand the theory, I just do not agree with it.
Hawking’s theory basically asserts that the intense gravitational field is able to pull energy out of the quantum vacuum, and that the vacuum in turn can pull mass/energy out of the black hole (or to be more accurate, out of the black hole and into a vacuum void that exists inside of the black hole. But then the vacuum energy itself still has to be able to pervade the boundary of the event horizon. The theory wants to claim that the black hole can still take in “negative energy” on its surface. But wouldn’t this “negative” energy actually be repelled by the gravitational forces?

Then where exactly did this energy exist before it was radiated?
Mass (not necessarily rest mass) accompanies energy, so if the black holes lose orbital energy they also lose mass. Where was this mass stored, exactly?

It was stored in the orbital motion.

So you are saying this energy was not inside the black hole?
One would be inclined to think that all the mass in this system is inside either of the two black holes.
Are you saying that a form of mass exists outside the event horizons of the black holes??

This has actually been observed, not in black holes, but nearby large atomic nuclei. Take an Uranium nucleus: near it, empty space can break down, emitting Hawking radiation, because of the large gravitational gradient near the nucleus.

(Scientific American, “Decay of the Vaduum.”)

This isn’t just theoretic: it’s actual observed fact.

How does the charge escape from the hole?

Charge doesn’t “escape.” Charge emanates. Charge is a surrounding field.

An electron doesn’t “leak” electric charge: electric charge surrounds the electron, coming from it. Same with a charged black hole: the hole itself is charged.

According to Quantum Electrodynamics, charge is carried by virtual photons. But since we never see them – they’re virtual – the electric field acts like a force field, obeying Maxwell’s laws.

Let’s get this clear: nothing escapes from a black hole, it’s the definition of a black hole. Now it maybe that in a full theory of quantum gravity true black holes (i.e. formally speaking regions causally-disconnected from future null infinity) are impossible, however classically there isn’t much room for debate.

A more interesting question is whether black holes can absorb em radiation at wavelengths greater than the Schwarzschild radius. The answer appears to be mostly no, the vast majority incoming em radiation with wavelength greater than the the Schwarzschild radius will be scattered rather than absorbed by a BH.

That is a fascinating line of thinking.
I have seen theories out there suggesting that electrons might actually be analogous to tiny black holes. This could potentially explain why such a particle would not be able to “suck up” a photon. But it seems charged black holes have no problem absorbing or emitting energy from their orbital momentum.