Black holes with infinitely degenerate horizons are proposed to be stable against Aretakis instability, potentially serving as end states.
McMaken,Semiclassical instability of inner-extremal regular black holes,Phys
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Taming the Aretakis instability: extremal black holes with multi-degenerate horizons
Black holes with infinitely degenerate horizons are proposed to be stable against Aretakis instability, potentially serving as end states.