Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The condition of being extremal
Etymologies
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Examples

In an extremal black hole, where all of the energy comes from the electric field itself, the two horizons coincide: we have r+ = r  (extremality).

We found that the volume of spacetime between the two horizons approached a smooth limit as the charge was increased, but discontinuously disappeared exactly at extremality.

In other words, the approach to extremality is not continuous, as the nonextremal ReissnerNordström solution splits into two spacetimes at extremality: an extremal black hole and a disconnected $AdS$ space.

Hawking, Horowitz and Ross found that the entropy of a charged black hole approached a smooth limit as the charge was increased, but discontinuously went to zero exactly at extremality.

Quick question: if the limit of approaching extremality is discontinuous, doesn't that mean that the exactly extremal space, the one with zero entropy, is unstable to infinitesimal perturbations, and therefore unphysical?

But Matt, Lisa and I stumbled across an interesting miracle of curved spacetime, which I think some people recognized but certainly isn't widely appreciated: as you creep up on extremality, increasing the charge of the black hole while keeping its mass fixed, and therefore driving

But Matt, Lisa and I stumbled across an interesting miracle of curved spacetime, which I think some people recognized but certainly isn’t widely appreciated: as you creep up on extremality, increasing the charge of the black hole while keeping its mass fixed, and therefore driving r  ever closer to r+, the spacetime volume of the region in between them does not go to zero.

The higher variance implies that it is easier to find more extreme men than more extreme women, regardless of the exact quantity that defines the extremality.”
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