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For charged black holes, supposing true the cosmic censorship conjecture, this inequality must be verified (in natural units):

$GM^2 > Q^2$

Where of course $M$ and $Q$ are the mass and charge of the black hole. Now suppose you "throw" a bunch of charged particles into the black hole. I know that the definition of charge and mass of a black hole is complicated and I know almost nothing about those. What I know is that they are usually defined based on their asymptotic values far away from the hole.

A quick google search seems to tell me that a particle falling into the black hole cause its mass and charged to increase of the mass and charged of the particle.

Does this mean that the inequality imply a limit for the mass/charge ratio for charged particles? Because if there's no limit one could keep throwing particles with a specific ratio until the inequality is no longer true creating a naked singularity.

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  • $\begingroup$ Related: physics.stackexchange.com/q/61118/2451 , physics.stackexchange.com/q/6650/2451 , physics.stackexchange.com/q/15517/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Sep 22 '16 at 14:25
  • $\begingroup$ Which natural units? $\endgroup$
    – Sean E. Lake
    Sep 22 '16 at 14:46
  • $\begingroup$ It has already been answered and accepted. And it is a good answer. Why not take it off the bounty list? Nobody is going to waste their time if they may have any interest on the bounty. Of course, somebody with a different answer, if it was correct, would get the bounty, and actually counter well accepted previous results by Wald, and many others doing calculations later. So it'd be a real coup. But if it was me I'd publish that in Phys Rev or Letters instead. So, call this bounty claimed. $\endgroup$
    – Bob Bee
    Sep 24 '16 at 5:38
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No, this does not imply a charge/mass limit, but this is a really interesting question, and was answered for the first time in a famous paper of Wald from 1974.

His paper showed that, at least in the specific case where the charge of the particle is much smaller than the charge of the black hole, any particle with a charge/energy ratio that could result in a naked singularity if it were absorbed by the black hole will, in fact, be deflected before it reaches the event horizon. So there is no limit on the charge/energy ratio of the particle itself due to cosmic censorship, but there IS a limit on what kinds of particles can actually be absorbed by the black hole. That limit corresponds exactly to the limit needed to preserve cosmic censorship (at least in the case of an extremal black hole).

A 1999 paper due to Hubeny (http://arxiv.org/abs/gr-qc/9808043) raised some new questions about this result by looking at potential higher-order problems when one considers black holes that are nearly-extremal rather than extremal. This potential issue was seemingly resolved by Poisson and collaborators in 2013 (http://arxiv.org/abs/1211.3889).

NB: You may notice that I wrote "charge/energy" rather than "charge/mass" when discussing the particle's parameters. This is no mistake—the mass change in the black hole when it absorbs a particle is governed by the particle's total energy, not its rest mass. Even if you make a black hole absorb a particle with an arbitrary high charge and arbitrarily small rest mass, for example by pushing the particle to the edge of the event horizon with a rocket ship, the particle will pick up enough energy over the course of the "pushing" process to counterbalance its charge and preserve cosmic censorship.

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