The Kerr black hole as a quantum rotator

Abstract

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. (The procedure employs a periodicity condition that can be viewed as a conjectural, although well-motivated input.) 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 An,Jcl = 8πℏ(n + Jcl + 1/2), where n and Jcl are both integers. The quantum number Jcl 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 Jcl ≫ 1, Jcl ≈ j.