Universal near-horizon conformal structure and black hole entropy

TL;DR

This paper demonstrates that many black holes share a universal near-horizon conformal structure, linking their entropy to a specific CFT with deep algebraic symmetries, including the monster group, beyond the traditional AdS/CFT framework.

Contribution

It introduces a universal algebraic approach revealing a common near-horizon conformal structure for various black holes, connecting their entropy to the FLM model and the monster group.

Findings

Universal near-horizon conformal structure for various black holes

Connection between black hole entropy and the FLM model

Lower bound on entropy established for a broad class of black holes

Abstract

It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer-Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes in our formalism can be identified with the FLM model, although not through the AdS/CFT correspondence. The corresponding entropy for the BTZ provides a lower bound for the entropy of this entire class of black holes.