The quantum mass gap of extremal black holes

TL;DR

This paper demonstrates that the mass gap of near-extremal Reissner-Nordström black holes can be derived through a semi-classical approach, confirming previous string theory results about their finite energy gap.

Contribution

It provides a simple semi-classical proof of the quantum mass gap for near-extremal charged black holes, complementing complex string theory calculations.

Findings

The mass gap is ${ m E}_{ ext{gap}}=\hbar^2/M^3$.

The mass gap is finite and characteristic of near-extremal black holes.

Semi-classical analysis suffices to determine the mass gap.

Abstract

Using sophisticated string theory calculations, Maldacena and Susskind have intriguingly shown that near-extremal black holes are characterized by a {\it 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 ${\cal E}_{\text{gap}}=\hbar^2/M^3$, which characterizes the mass spectra of near-extremal charged Reissner-Nordstr\"om black holes, can be inferred from a simple semi-classical analysis.