In theoretical physics, an extremal black hole is a black hole with the minimal possible mass that can be compatible with a given charge and angular momentum. In other words, this is the smallest possible black hole that can exist while rotating at a given fixed constant speed with some fixed charge.
The concept of an extremal black hole is theoretical and none have thus far been observed in nature. However, many theories are based on their existence.
In supersymmetric theories, extremal black holes are often supersymmetric: they are invariant under several supercharges. This is a consequence of the BPS bound. Such black holes are stable and emit no Hawking radiation. Their black hole entropy can be calculated in string theory.
It has been suggested by Sean Carroll that the entropy of an extremal black hole is equal to zero. Carroll explains the lack of entropy by creating a separate dimension for the black hole to exist within.
The Hawking radiation of extremal black holes are considered non-thermal (non-Planck distributed), with no associated temperature.
The hypothetical black hole electron is super-extremal (having more charge and angular momentum than a black hole of its mass "should").