The statistical mechanics of near-extremal black holes

DOI10.1007/JHEP05(2021)145zbMATH Open1466.83053arXiv2003.02860OpenAlexW3161344359MaRDI QIDQ2048014

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Publication date: 4 August 2021

Published in: (Search for Journal in Brave)

Abstract: An important open question in black hole thermodynamics is about the existence of a "mass gap" between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this paper, we reliably compute the partition function of Reissner-Nordstr"{o}m near-extremal black holes at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge does not exhibit a gap; rather, at the expected gap energy scale, we see a continuum of states. We compute the partition function in the canonical and grand canonical ensembles, keeping track of all the fields appearing through a dimensional reduction on $S^2$ in the near-horizon region. Our calculation shows that the relevant degrees of freedom at low temperatures are those of $2d$ Jackiw-Teitelboim gravity coupled to the electromagnetic $U(1)$ gauge field and to an $SO(3)$ gauge field generated by the dimensional reduction.

Full work available at URL: https://arxiv.org/abs/2003.02860

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