Extremal black holes are at zero temperature, hence they do not radiate.

My question is twofold:

  1. 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)?

  2. 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?

  • 1
    $\begingroup$ 1) Extremal black holes are always unstable (in standard GR at least, I can't speak for string theory etc) e.g. see arxiv.org/abs/1206.6598. 2) Yes, a black hole can gain/lose charge/angular-momentum due to in-falling matter. In theory it'd be possible to add charged matter to make a Kerr black hole become extremal, and matter of the opposite charge to do the inverse, etc. $\endgroup$
    – Eletie
    Dec 13, 2020 at 23:25

1 Answer 1


In the context of supersymmetric extremal black holes:

1.- Extremality is stable under the change of black hole radius (as far as the radii is not too close to the Planck length).

2.- An extremal black hole can be made non-extremal by probing it with objects such that the (probes + extremal black hole) bound state breaks 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 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 "destroyed by stringy corrections" (Reference: Xi Yin, Strings 2013)). If they don't really exist, you may be able to produce non-extremal black holes by perturbing extremal ones with available 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 upvoted 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 keep the angular momentum to mass squared ratio less than one - that is, non-extremal.

Edit: By "probing 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 compactfied on $\mathcal{T}^4$ $ \times $ $\mathcal{S}^1$ that means studying the black hole solution on a non-trivial $D$(-1) instanton background (this was done here in a T-duality related case).

A nice example of how an extremal $D3$- black branes are made non-extremal is discussed at section 3.2 in these lecture notes, (alternative link). Another set of nice results that analyze non-extremal 4D black hole solutions, with $\mathcal{N}=2,4,8$,by embedding them on non-trivial backgrounds is Non-supersymmetric Black Holes and Topological Strings. Both cases are examples of extremal black hole solutions "being probed": being made non-extremal by coupling them to non trivial backgrounds, or adding anti-branes.

  • $\begingroup$ This answer is hard to understand. What does "proving it with objects" mean? $\endgroup$
    – PM 2Ring
    May 9, 2020 at 6:40
  • $\begingroup$ Sorry, it was not my intention to confuse you. I added an edit to my answer in order to try to satisfy your observation. $\endgroup$ May 10, 2020 at 19:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.