A Merger of Extremal BHs Causes Naked Singularity?

[arusse02]

Let's say you have two extremal black holes containing the maximum amount of possible charge. Now let's say they're orbiting each other such that they will eventually merge. As the black holes merge they are producing gravitational waves. Once the merger is complete the new black hole mass will be less than the sum of the original two masses when they were separate. However, at this point, where did the extra charge the black holes contained go? Is there some sort of mechanism where the new black hole will have lost charge in proportion to the mass it lost during the merger? If the mass decreases, but the charge remains the same, then wouldn't there have to be a naked singularity?

 

[martinbn]

I don't know if there are results in this direction, but there are papers (I have to look for them) that analyze whether you can overspin an extremal Kerr, or if you can overcharge an extremal charged black hole. The conclusions are that you cannot. It may be the wrong intuition but you can think about as this: if they have charge of the same sign, they will repel electromagnetically, they will not just attract gravitationally, so if the result would be a naked singularity, it would be impossible, they will not merge.

 

[martinbn]

I found the paper that I had in mind

Wald, Gedanken experiments to destroy a black hole

But one can also find papers which show that under certain assumptions it is possible to overcharge or overspin a black hole.

https://arxiv.org/abs/gr-qc/9808043

We show that, contrary to a widespread belief, one can overcharge a near extremal Reissner-Nordstrom black hole by throwing in a charged particle, as long as the backreaction effects may be considered negligible. Furthermore, we find that we can make the particle's classical radius, mass, and charge, as well as the relative size of the backreaction terms arbitrarily small, by adjusting the parameters corresponding to the particle appropriately. This suggests that the question of cosmic censorship is still not wholly resolved even in this simple scenario. We contrast this with attempting to overcharge a black hole with a charged imploding shell, where we find that cosmic censorship is upheld. We also briefly comment on a number of possible extensions.

https://arxiv.org/abs/0907.4146

It has long been known that a maximally spinning black hole can not be over-spun by tossing in a test body. Here we show that if instead the black hole starts out with below maximal spin, then indeed over-spinning can be achieved when adding either orbital or spin angular momentum. We find that requirements on the size and internal structure of the test body can be met as well. Our analysis neglects radiative and self-force effects,which may prevent the over-spinning.

 

[PeterDonis]

one can also find papers which show that under certain assumptions it is possible to overcharge or overspin a black hole.

I think it would be more accurate to say that these papers raise the possibility of overcharging or overspinning a black hole, and give an initial analysis which appears to support such possibilities, but then cast doubt on the initial analysis by pointing out that it treats the infalling object as a test body, but that that is not really correct, and when one tries to take into account the non-test-body effects that must be present, one finds that, while the resulting equations cannot be solved analytically, most likely they will result in the infalling object not overcharging or overspinning the hole: the object will either "bounce" instead of falling in, or will lose enough angular momentum that it no longer overspins the hole.