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-Nordström 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 S2 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.
Highlights
Extremality, black holes have zero temperature, mass M0, and area A0
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
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
Summary
We will focus on several kinds of 4d black hole solutions. we will consider the Reissner-Nordström black holes solutions and Kerr-Newman solutions of low spin, in both asymptotically AdS4 spaces and flat spaces. We will pick boundary conditions dominated by solutions with a large charge at low temperatures, in the regime where the black hole will be close to extremality. The first is the limit L → ∞ where we recover a near-extremal black hole in flat space, and large Q In this case the mass and entropy scale with the charge as r0 ∼ PLQ,. As the temperature is taken to zero this region keeps being well approximated by the semiclassical geometry This is appropriate for the case of large black hole limit in AdS4. For the case of black holes in the flat space limit, we take L → ∞ of the metric above, finding the extremal geometry in asymptotically flat space Both the NHR and the FAR region overlap inside the bulk.
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