Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Mathematics Of or relating to maximal or minimal values or degrees of inclusiveness.
 adj. Having or characterized by extreme properties or conditions: an extremal black hole.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Having to do with extrema.
 n. Any solution to a variety of equations in the calculus of variations
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

Penrose hypothesizes that the extremal is a graviton.

It is disingenious to ascribe every heat wave to global warming but explain away all extremal cold events as "just weather".
Giving evidence to the Chilcot inquiry, Tony Blair said: “I...

If it works – even on a rudimentary level – Hameroff will be vindicated, and it won't matter at all that nobody knows what the extremal is.

But at current and projected scientific abilities I cannot expect much more than what's offered – a collapsing extremal of baseline fundamental nature, even if there's no such thing as actually collapsed extremals.

I suspect there is some extremal principle here, where the tuning is some variational principle on a partition function which results in a greatest upper bound on the measure of complexity which can exist in a local region.
Death in the Sky: M31 Shreds its Satellites  Universe Today

Perhaps the states disappear into Whoville, rather than really describing an extremal black hole.

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.

They calculated the entropy of black holes with electric charge, and in particular of extremal black holes — configurations where all of the energy really comes from the electric field itself, none from any purported mass that might have fallen into the black hole.

We suggest that the unusual nature of this limit may help in understanding the entropy of extremal black holes.

The best argument against it is the kind of microstate counting from string theory pioneered by Strominger and Vafa — they were always looking precisely at the extremal case, and found a nonzero entropy.
Comments
Log in or sign up to get involved in the conversation. It's quick and easy.