TL;DR
This paper explores the quantum statistics of extremal black holes, proposing they follow infinite statistics rather than Bose or Fermi, due to their unique quantum state structure involving wormholes.
Contribution
It introduces a hypothesis that extremal black holes obey infinite statistics, a novel idea differing from traditional quantum statistics, based on their geometric and topological properties.
Findings
Extremal black holes do not follow Bose or Fermi statistics.
They obey an exotic form of infinite statistics.
The statistics are modeled via a $q$-deformation of quantum commutation relations.
Abstract
The quantum statistics of charged, extremal black holes is investigated beginning with the hypothesis that the quantum state is a functional on the space of closed three-geometries, with each black hole connected to an oppositely charged black hole through a spatial wormhole. From this starting point a simple argument is given that a collection of extremal black holes obeys neither Bose nor Fermi statistics. Rather they obey an exotic variety of particle statistics known as ``infinite statistics'' which resembles that of distinguishable particles and is realized by a -deformation of the quantum commutation relations.
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