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 $J_{ cl}\gg 1$, $J_{ cl}\approx j$.
Categories: gr-qc hep-th quant-ph