Black hole entropy calculations based on symmetries

TL;DR

The paper reexamines symmetry-based explanations of black hole entropy in the 2+1D BTZ context, identifying and correcting technical flaws in prior work to develop a consistent near-horizon symmetry framework. It contrasts intrinsic horizon symmetries, which give zero central charge, with extended near-horizon vector fields on a stretched horizon that produce a Virasoro-like algebra with a finite central term, yielding a Cardy-based entropy. The resulting entropy is proportional to the horizon area but differs from the Bekenstein-Hawking value by a factor of $\sqrt{2}$, suggesting that the central charge is fundamentally quantum mechanical in origin and that a full quantum treatment (not a purely classical horizon analysis) is required. Overall, the work clarifies the limits of classical symmetry methods for black hole entropy and highlights the role of quantum regularization in determining the correct entropy.

Abstract

Symmetry based approaches to the black hole entropy problem have a number of attractive features; in particular they are very general and do not depend on the details of the quantization method. However we point out that, of the two available approaches, one faces conceptual problems (also emphasized by others), while the second contains certain technical flaws. We correct these errors and, within the new, improved scheme, calculate the entropy of 3-dimensional black holes. We find that, while the new symmetry vector fields are well-defined on the ``stretched horizon,'' and lead to well-defined Hamiltonians satisfying the expected Lie algebra, they fail to admit a well-defined limit to the horizon. This suggests that, although the formal calculation can be carried out at the classical level, its real, conceptual origin probably lies in the quantum theory.