An extremal black hole lies at the parameter bound where its inner and outer horizons coincide. Its surface gravity and hence its semiclassical Hawking temperature vanish.
At a degenerate static horizon the Euclidean proper radial distance diverges logarithmically, so the horizon is an infinite end rather than a finite polar origin. Its time circle is not contracted at a conical tip, and local cone regularity imposes no finite period. The vanishing limiting surface gravity determines zero Hawking temperature; the simple-horizon periodicity argument must not be applied unchanged at the degenerate root.
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An extremal black hole is a type of black hole that exists at the limit of certain physical parameters, particularly when considering its mass and charge or angular momentum. In the context of general relativity and modern theoretical physics, extremal black holes are characterized by having their mass equal to a specific value where they cannot radiate further or absorb additional charge or angular momentum without becoming non-extremal.