Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy

TL;DR

This paper uses an algebraic approach to quantum black holes to derive logarithmic corrections to black hole entropy, showing that hyperspin must be zero and refining the degeneracy of area eigenvalues.

Contribution

It introduces a symmetry-based algebraic framework for black hole quantization, revealing a hyperspin constraint and deriving entropy corrections.

Findings

Hyperspin of the black hole must be zero.

Degeneracy of area eigenvalues is reduced by a factor of n^{3/2}.

Logarithmic correction to Bekenstein-Hawking entropy is -3/2 log A.

Abstract

The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral non-rotating black hole, such eigenvalues must be $2^{n}$-fold degenerate if one constructs the black hole stationary states by means of a pair of creation operators subject to a specific algebra. We show that the algebra of these two building blocks exhibits $U(2)\equiv U(1)\times SU(2)$ symmetry, where the area operator generates the U(1) symmetry. The three generators of the SU(2) symmetry represent a {\it global} quantum number (hyperspin) of the black hole, and we show that this hyperspin must be zero. As a result, the degeneracy of the $n$-th area eigenvalue is reduced to $2^{n}/n^{3/2}$ for large $n$, and therefore, the logarithmic correction term $-3/2\log A$ should be added to the Bekenstein-Hawking entropy. We also provide a heuristic approach explaining this result, and an evidence for the existence of {\it two} building blocks.