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.
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.[3]
The Hawking radiation of extremal black holes is considered non-thermal (non-Planck distributed), with no associated temperature.[4]
The hypothetical black hole electron is super-extremal (having more charge and angular momentum than a black hole of its mass "should").
The third law of black hole thermodynamics should disallow such an extremal black hole and in 1986 a proof was published[5] by Werner Israel. Nevertheless, recent work in a pair of preprints claims it contains an error and therefore extremal black hole are indeed possible.[6][7][8] The third law of thermodynamics for black holes has always been controversial.
^Kehle, Christoph; Unger, Ryan (2023-04-17). "Event horizon gluing and black hole formation in vacuum: the very slowly rotating case". arXiv:2304.08455 [gr-qc].
^Kehle, Christoph; Unger, Ryan (2024-02-15). "Extremal black hole formation as a critical phenomenon". arXiv:2402.10190 [gr-qc].
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