Quantum Spectrum for a Kerr-Newman Black Hole

TL;DR

This paper derives a quantum area spectrum for Kerr-Newman black holes, showing it is evenly spaced and relates charge, spin, and mass quantum numbers, extending previous work on simpler black hole models.

Contribution

It generalizes the quantum area spectrum to Kerr-Newman black holes, revealing a unified, evenly spaced spectrum involving three quantum numbers and their interrelations.

Findings

Confirmed a uniformly spaced quantum area spectrum for Kerr-Newman black holes.

Derived selection rules linking charge and spin spectra.

Expressed the area operator in terms of three quantum numbers.

Abstract

In this paper, we consider the quantum area spectrum for a rotating and charged (Kerr-Newman) black hole. Generalizing a recent study on Kerr black holes (which was inspired by the static-black hole formalism of Barvinsky, Das and Kunstatter), we show that the quantized area operator can be expressed in terms of three quantum numbers (roughly related to the mass, charge and spin sectors). More precisely, we find that $A=8\pi\hbar[n+{1\over 2}+{p_1\over 2}+p_2]$, where $n$, $p_1$ and $p_2$ are strictly non-negative integers. In this way, we are able to confirm a uniformly spaced spectrum even for a fully general Kerr-Newman black hole. Along the way, we derive certain selection rules and use these to demonstrate that, in spite of appearances, the charge and spin spectra are not completely independent.