Kerr Black Hole as a Quantum Rotator

Details Kerr Black Hole as a Quantum Rotator Kerr Black Hole as a Quantum Rotator

2002-11-26

arxiv.org/abs/gr-qc/0211089v1

Class.Quant.Grav. 20 (2003) 2261-2274

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, Revtex

Scientific paper

10.1088/0264-9381/20/11/321

It has been proposed by Bekenstein and others that the horizon area of a black hole conforms, upon quantization, to a discrete and uniformly spaced spectrum. In this paper, we consider the area spectrum for the highly non-trivial case of a rotating (Kerr) black hole solution. Following a prior work by Barvinsky, Das and Kunstatter, we are able to express the area spectrum in terms of an integer-valued quantum number and an angular-momentum operator. Moreover, by using an analogy between the Kerr black hole and a quantum rotator, we are able to quantize the angular-momentum sector. We find the area spectrum to be $A_{n,J_{cl}}=8\pi\hbar(n+J_{cl}+1/2)$, where $n$ and $J_{cl}$ are both integers. The quantum number $J_{cl}$ is related to but distinct from the eigenvalue $j$ of the angular momentum of the black hole. Actually, it represents the ``classical'' angular momentum and, for $J_{cl}\gg 1$, $J_{cl}\approx j$.

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