What would happen if I kept pouring electrons down a black hole?

[Dorfl]

From what high school physics has taught me, the gravitational attraction in a singularity approaches infinity as its size approaches zero. This makes it impossible for anything to leave the black hole, except hawking radiation.

But what if I kept pouring electrically charged particles down the hole. Wouldn't their repulsion also approach infinity, and - since electromagnetic forces are stronger than gravitational at short distances - eventually overpower gravity?

There is probably some reason why this wouldn't work, but what is it?

[RecoveringYuppy]

The black hole would acquire a charge making it both repel electrons at some point and attract protons, negating the charge.

[Dorfl]

The black hole would acquire a charge making it both repel electrons at some point and attract protons, negating the charge.

But, how can the black hole electrically repel or attract matter?

Shouldn't it be impossible for the required virtual photons to leave it in the first place?

[Yllanes]

Your objection (electrostatic repulsion) could also be applied to the phenomenon of gravitational collapse. I'm sure someone with more time than I have at the moment can summarise how this happens.


Shouldn't it be impossible for the required virtual photons to leave it in the first place?

You might as well ask how does the gravity get out of the black hole (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html) (sci.physics FAQ).

[tracer]

But what if I kept pouring electrically charged particles down the hole. Wouldn't their repulsion also approach infinity, and - since electromagnetic forces are stronger than gravitational at short distances - eventually overpower gravity?


Assuming that mutual self-repulsion even works at ALL on the other side of an Event Horizon....

[ben m]

General Relativity contains a complete account of charge and (classical) electromagnetism as well as gravity. Black holes can have mass, spin, and charge; the special case of a charged, non-rotating black hole is called a "Reissner-Nordström" hole, and a black hole with both charge and spin is called "Kerr-Newman". If I recall correctly, it's impossible to increase the charge-to-mass ratio beyond a certain point, because the electrons are electrostatically repelled before they reach the event horizon.

[Thabiguy]

But, how can the black hole electrically repel or attract matter?

Shouldn't it be impossible for the required virtual photons to leave it in the first place?

I think this page (http://helios.gsfc.nasa.gov/qa_sp_bh.html#gravitons) contains the answer to that. I quote for convenience:
It is known that black holes can have charge, and therefore a static electric field. The question is, how does this field escape the horizon? In that, I should remind you that the horizon is the surface through which one cannot send any signals. Now, signals (i.e. photons) involve time changing fields. Indeed no such signal can come out of the horizon. However, the electrostatic field of a charge does not convey any signal; it can therefore escape from the black hole. In technical parlance it is a space-like object, and those can cut across horizons. Or differently, in the language of excitations of the electromagnetic field (the photons)- there are transverse and longitudinal photons. The transverse ones are those we see, and travel at the speed of light. The longitudinal ones are those which "are there" in space, they do not convey any signal and are the static fields of the charges.

Now as for the original question:
But what if I kept pouring electrically charged particles down the hole. Wouldn't their repulsion also approach infinity, and - since electromagnetic forces are stronger than gravitational at short distances - eventually overpower gravity?

In my opinion, no - the repulsion would not approach infinity. It would get bigger and bigger as you pour more electrons, it could possibly get very large, perhaps arbitrarily large, but it would remain finite. The electrostatic potential energy - the energy available for "pushing away" the particle - would be finite for any non-zero distance from the charged singularity - but the energy required to escape from the event horizon (which is at non-zero distance from the singularity) is infinite, therefore always bigger than anything one can muster by pouring charge particles in.

Disclaimer: I'm not 100% sure if this answer is correct - specifically, whether the classical formula for electrostatic potential energy isn't somehow changed by the extreme circumstances in the vicinity of the black hole. If I'm wrong, I'm sure someone more knowledgeable will correct me.

[Dorfl]

Oh, thanks.

I think I understood that. Or will, once I have looked through the various links.

[Complexity]

A larger black hole.

Go ahead and munch a bunch - We'll make more.

[Dabljuh]

I think I can follow the OP's reasoning, although I'm afraid I can't fully answer the question.

Consider a black hole of 1 kg weight. This means it would not exert any noticeable gravitational pull to a person, and Its schwarzschild radius is in the nanometers, but the potential charge of 1kg of mass can be high enough to violently repel electrons.

The electromagnetic force has the same range as the gravitational force. This means at a large distance, an equally larger black hole with a proportionally higher charge could and would have electromagnetic forces for an electron far exceeding gravitational forces.

Now what if I am to construct a black hole of say, the mass of the earth, but with precisely enough charge to negate the gravitational force to an individual electron? Would it be possible for the electron to, essentially, move through the black hole unaffected?

Unfortunately not. Because the notion of gravitation being a force is a newtonian concept, the relativity theory makes gravitation an intrinsic property of spacetime, which by itself would change how the magnetic field operates.

[Wiki]pedia has some articles on how charged black holes differ from uncharged ones. Essentially they end up with multiple event horizons. I think You'd have to do the actual calculations to figure out at what distance an electron would be repelled, and at what distance it would be sucked into the singularity.

Please remember the injunction against swearing. I have edited the offensive word.