Expert: James Gort - 6/11/2009

Question
Since not even light can escape the event horizon of a black hole, if a black hole managed to accumulate a strong surplus of positive charge beyond the event horizon, would there (or not) be an electric field that would tend to force it back into charge balance (beyond the event horizon)?

Answer
Hi Tom,

I'm not quite sure I understand your question.  I'll assume "beyond" the event horizon means "outside" the event horizon.  Because inside the event horizon, we have no knowlegde of what's taking place.  So the picture I have in my mind is a black hole, surrounded by a shell of positive charge.  Is that correct?  That's not too likely a scenario, but we'll use that as our starting point.  Is the black hole itself charged?  There's only three parameters that completely define a black hole - mass, charge, and angular momentum.  And they must obey the relation (GM/c)^2 >= G (Q/c)^2 + (J/M)^2.  Nothing can violate that inequality without destroying the black hole - it would become a naked singularity!  

So if the black hole were negatively charged, there would be an electric field between the event horizon and the positive cloud.  The cloud would be sucked in, tending to make the hole less negative.

If the black hole was positively charged, and the inequality was close - that's a more interesting story.  Because gravity would try to suck the charged particles in, but Coulomb repulsion would try to keep them out.  Well, it so happens that Coulomb repulsion wins, since we can't violate the inequality!

Hope that helps.  If I've misunderstood your question, please ask again.

Prof. James Gort