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

作者：Gour G^*

来源：Physical Review D – Particles and Fields, 2002, 66(10): 104022.

DOI：10.1103/PhysRevD.66.104022

The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral nonrotating 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)equivalent toU(1)xSU(2) symmetry, where the area operator generates the U(1) symmetry. The three generators of the SU(2) symmetry represent a 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 evidence for the existence of two building blocks.

• 出版日期2002-11-15