Abstract. In a gravitational theory with a massless photon the maximum charge-to-mass ratio of black holes approaches the prediction of the Einstein-Maxwell theory as black hole mass increases: Q_ext/M = 1 + a/ M^2 for some constant a. I will show that a>0 if below the quantum gravity scale (\Lambda) there are many degrees of freedom with a hierarchically small mass gap, log(\Lambda/m)>>1. In this regime one can derive field-theoretic sum-rules for the coefficients of the leading corrections to the Einstein-Maxwell theory that imply a>0. Hence gravitational force among maximally charged black holes keeps getting weaker than the electric force as the black hole size becomes smaller.
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