Black hole entropy calculations based on symmetries

TL;DR

This paper evaluates symmetry-based methods for calculating black hole entropy, identifies flaws in existing approaches, corrects them, and computes entropy for 3D black holes, highlighting conceptual issues in the classical limit.

Contribution

It corrects technical flaws in symmetry-based entropy calculations and explores their limitations, emphasizing the quantum nature of the underlying conceptual framework.

Findings

Symmetry vector fields are well-defined on the stretched horizon.

Hamiltonians satisfy the expected Lie algebra.

Limit to the horizon is not well-defined in the classical scheme.

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.