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The Gravity Field of an Extremal Black Hole
The idea of an extremal black hole has to do with the fact that black holes are characterized by their mass, charge, and spin. If you're an uncharged particle, if you are not yourself electrically charged, then you will just fall into the black hole. There's a discontinuity in the internal spacetime structure as you go from a regular black hole to an extremal one. It's right barely at the point where there might be naked singularity, but there isn't really. They're interesting things for theorists to think about.