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What would happen if we have a black hole and we start shooting at it a single electron at a time, and go on doing it forever? Would the electrons start to bounce off eventually?

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Related: – Qmechanic Oct 8 '11 at 14:38
up vote 6 down vote accepted

There is a limit on how much charge a black hole may have:

In general, rotating, charged black holes is described by a Kerr-Newman metric.

Intuitively, eventually the Coulumb repulsion is enough that a charged particle which does not contribute more mass than charge will be repelled.

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This is not intuitive, it is exact. – Ron Maimon Nov 2 '12 at 17:35
Is there a reference or a theory or some place where this has been worked out in more detail? What happens when you accelerate charge up to near the speed of light and direct them at the black hole. Will an Extremal black hole really repulse the charge still? Is there a point where to get the charge into the black hole you have to add so much kinetic energy that the net result is that you're increasing mass (by way of energy) faster than you're increasing charge? – Brandon Enright Apr 15 '13 at 22:37

The Coulomb repulsion of the charged black hole does not prevent the charged black hole from acquiring more charge. If this were the case, then "all" that would be necessary to continue to charge a black hole would be to increase the energy of the beam of electrons that are shot at the black hole to overcome the Coulomb repulsion. You would just need bigger and bigger accelerators to keep charging the black hole up to and beyond the extremal limit. When the black hole exceeds the extremal limit it would become a naked singularity.

The concept or possibility of a naked singularity is controversial - it would allow actual "infinite" singularities to be seen directly in our universe - they would not be hidden behind an event horizon the way the singularity of an "ordinary" black hole is hidden. Indeed, a cosmic censorship hypothesis has been devised to prevent naked singularities from occurring. There is good evidence for this hypothesis but I don't believe it has been convincingly proven in all cases.

The real reason why adding charge to a black hole cannot make it become super-extremal is because when you add charge, you are also increasing the electrostatic field energy of the black hole which then has the effect of increasing the mass such that the $\frac{Q}{M}$ ratio continues to stay below the extremal limit of $1.0$. See this question and answer for the calculation of this effect.

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But the electrostatic field energy is equivalently the energy required to beam the particles into the black hole. As you approach the extremal limit, the required energy gets bigger, so that the particles always deposite at least as much mass as charge, pulling the hole away from extremality. – Ron Maimon Oct 24 '11 at 7:09
@Ron, By saying that it is not coulomb repulsion I am saying that the accepted answer for this question is wrong. It says the electron will be repelled away from the BH. I am saying that the electron can be made to enter the black hole but that the mass gained by the increased electrical field energy will add more mass and will prevent the black hole from becoming extremal. You are right that the kinetic energy that you had to impart on the electron to make it to the BH horizon is where the electric field energy comes from. Do you agree that the accepted answer is wrong about being repulsed? – FrankH Oct 25 '11 at 0:03
But this extra mass gained from electrical energy is supplied by the work required to push the electron in! This is exactly the same explanation as the usual one, in different language. I agree only that your explanation is just as correct as the usual one--- they are equivalent. – Ron Maimon Oct 25 '11 at 0:30

Fairly soon the electrons would repel the black hole in the newtonian area (i.e. far away). As it kept charged up, it would take more and more energy to bring the electrons close enough so that general relativity takes over and pulls them in. All this energy adds to the black hole mass, keeping it from becoming extremal.

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