The quantum mass gap of extremal black holes

Using sophisticated string theory calculations, Maldacena and Susskind have intriguingly shown that near-extremal black holes are characterized by a finite mass gap above the corresponding zero-temperature (extremal) black-hole configuration. In the present compact paper we explicitly prove that the minimum energy gap $E_{\text{gap}}={ħ}^2/M^3$, which characterizes the mass spectra of near-extremal charged Reissner-Nordström black holes, can be inferred from a simple semi-classical analysis.