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The Weak Gravity Conjecture Requires the Existence of Exotic AdS Black Holes
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abstract
The Weak Gravity Conjecture arises from the requirement that it be possible for all (classically stable) extremal black holes to decay. The ``black hole version'' of the conjecture requires that it should be possible for this to occur through the emission of smaller black holes. We consider this version in the case of extremal AdS$_4$-Kerr-Newman black holes which are stable against a superradiant instability. One finds that the emitted black hole must be rather exotic, having an ``angular horizon'' analogous to the more familiar (radial) horizon.
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Quantum Corrections and Extremality: A Generalized Universal Relation
For any entropy function S(r_h), the Goon-Penco extremality ratio equals d(pi r_h^2)/dS, so the original relation survives only for the area law.
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