Kerr Black Hole as a Quantum Rotator

TL;DR

This paper derives a quantized area spectrum for Kerr black holes by modeling them as quantum rotators, linking horizon area to quantum numbers and angular momentum, and providing a discrete spectrum formula.

Contribution

It introduces a novel approach to quantize Kerr black hole horizons using an analogy with quantum rotators, extending previous area quantization models.

Findings

Derived the area spectrum as A_{n,J_{cl}}=8πħ(n+J_{cl}+1/2)

Connected classical angular momentum J_{cl} with quantum number j for large J_{cl}

Extended area quantization to rotating black holes using angular-momentum operators

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. 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 $J_{cl}\gg 1$, $J_{cl}\approx j$.