On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry

TL;DR

This paper argues for the SU(2) gauge group in loop quantum gravity by linking fermion principles to black hole entropy and quasinormal mode predictions, providing a physical basis for the Immirzi parameter choice.

Contribution

It offers a simple physical argument within loop quantum gravity supporting SU(2) as the gauge group, aligning black hole entropy and quasinormal mode predictions.

Findings

Supports SU(2) as the relevant gauge group

Provides a physical argument for the Immirzi parameter

Links fermion principles to black hole properties

Abstract

Loop quantum gravity can account for the Bekenstein-Hawking entropy of a black hole provided a free parameter is chosen appropriately. Recently, it was proposed that a new choice of the Immirzi parameter could predict both black hole entropy and the frequencies of quasinormal modes in the large $n$ limit, but at the price of changing the gauge group of the theory. In this note we use a simple physical argument within loop quantum gravity to arrive at the same value of the parameter. The argument uses strongly the necessity of having fermions satisfying basic symmetry and conservation principles, and therefore supports SU(2) as the relevant gauge group of the theory.