Physics Asked on June 28, 2021
To celebrate 10 upvotes but no attempt at answers of this 8-year old question regarding extremality of Reissner-Noström blackholes, Let’s formulate a physically feasible scenario for driving a galactic black hole well over extremality via charge injection
As it is estimated in the original question, a black hole with a little above 100 solar masses should be stable against Schwinger vacuum breakdown, meaning that adding enough charge to make the black hole extremal does not require to exceed the Schwinger vacuum breakdown electric field near the horizon
But the electric field scales inversely proportional to the BH mass squared, which means that for a galactic black hole (well above the order of millions of solar masses) the electric field can be well below what a physically realisable ion/electron source needs to put to throw charge into the BH from the asymptotic flat region.
If all assumptions are correct, then this scenario should enable to exceed extremality and expose singularities to the asymptotic region, which would led to all sort of unexpected phenomena
The only assumption I am unsure is that the Schwinger breakdown electric field is not affected by the gravitational field, but if there was some empirical squared relationship between surrounding mass and vacuum breakdown, the above conclusion would be avoidable
Is this conclusion avoidable? If not, could there be a theoretical foundation (hopefully within known semi-classical theory) to a vacuum breakdown relationship like:
$$ E_{text{Schwinger}} propto M^{2} $$
You cannot throw charge into a nearly extremal Kerr-Newman black hole to over charge (or over spin it.) This is simply dynamically impossible, and will be prevented by a combination plain old electric repulsion and the energy needed to get a charge into the black hole. This was proven in complete generality in this brilliant paper by Sorce & Wald.
(I might add a more complete answer latter, but for now, the Sorce&Wald paper is the definitive answer to your question.)
Answered by mmeent on June 28, 2021
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