Transition between extremal and non-extremal black hole states Extremal black holes are at zero temperature, hence they do not radiate.
My question is twofold:

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*Is extremality of micro black holes a stable property? Electric charge is quickly emitted from sub-atomic black holes due to Schwinger pair production, what about angular momentum? Does a black hole loses its extremality quickly or slowly (compared to its evaporation time)?


*Can a black hole extremality state be changed by external sources? Can we add matter and angular momentum appropriately to a Schwarzschild black hole in order for it to become extremal or nearly-extremal? Can we do the inverse process?
 A: 1.- Extremality is a stable under the change of black hole radii (as far as the radii is no to close to the Planck lenght).
2.- An extremal black hole can be made non-extremal by proving it with objects such that the proves + extremal black hole bound states broke some supersymmetries. An example of this could be the classical $D1$-$D5$ system with $D$(-1)-instantons or dyonic states in type IIB superstring theory or studying some  1/16 black hole solution in the Maldacena's $AdS_{5}$ $ \times $ $\mathcal{S}^5$ on a non-trivial D(-1) instanton background.
Recall that an interesting open problem is to discover if 1/16-BPS supergravity black hole solutions exist in full string theory or if they are "distroyed by stringy corrections" (Reference:
https://www.youtube.com/watch?v=QbyPI1MFbGA ). If they don't really exist, you may be able to produce non-extremal black holes by perturbing extremal ones with avaliable supersymmetric proves like D-instantons (instanton solutions for the near-horizon geometry of a stack of $D3$ branes) and breaking some supersymmetries until the 1/16 (or fewer) unstable situation is reached.
You can also read the most voted answer to the question Why Do Extremal Black Holes Not Radiate? The answer beautifully explains how galactic black holes of the Kerr-type "regulate themselves" by purely "mundane" astrophysical mechanisms in order to mantain its angular momentum to mass squared ratio smaller that the unity (the extremality regime).
Edit: By "proving it with objects" I meant to embed a particular black hole solution in a non trivial background with that particular object. In the famous $D5$-$D1$ system for type IIB strings compatfied on $\mathcal{T}^4$ $ \times $ $\mathcal{S}^1$ https://arxiv.org/abs/hep-th/0002184 that means to study the black hole solution on a non-trivial $D$(-1) instanton background (as was done here in a T-duality releated case).
A nice example of how an extremal $D3$- black brane are made non extremal is disscused at section 3.2 in https://www.ipht.fr/Docspht/articles/t12/003/public/2012_Bena+ElShowk_by_Vercnocke_All_Lectures.pdf. Another set of nice results that analyze non-extremal N=2,4,8 four dimensional black hole solutions by embedding them on non-trivial backgrounds is Non-supersymmetric Black Holes and Topological Strings. Both cases are examples of extremal black hole solutions made non-extremal by ("proving them") coupling them to non trivial backgrounds or adding anti-branes.
