Quanta of Geometry and Rotating Black Holes

Abstract

In the loop approach to quantum gravity the spectra of operators corresponding to such geometrical quantities as length, area and volume become quantized. However, the size of arising quanta of geometry in Planck units is not fixed by the theory itself: a free parameter, sometimes referred to as Immirzi parameter, is known to affect the spectrum of all geometrical operators. In this paper I propose an argument that fixes the value of this parameter. I consider rotating black holes, in particular the extremal ones. For such black holes the ``no naked singularity condition'' bounds the total angular momentum J by A_H/8 pi G, where A_H is the horizon area and G Newton's constant. A similar bound on J comes from the quantum theory. The requirement that these two bounds are the same fixes the value of Immirzi parameter to be unity. A byproduct of this argument is the picture of the quantum extremal rotating black hole in which all the spin entering the extremal hole is concentrated in a single puncture.

5 pages

References in corpus (1)

• Quantum Geometry and Black Hole Entropy

Cited by in corpus (13)

• Supersymmetric Spin Networks and Quantum Supergravity
• Black Hole Entropy, Loop Gravity, and Polymer Physics
• Canonical Quantization and the Statistical Entropy of the Schwarzschild Black Hole
• Black hole horizons from within loop quantum gravity
• Eleven dimensional supergravity as a constrained topological field theory
• Entropy calculation for a toy black hole
• A candidate for a background independent formulation of M theory
• Elementary charge and neutrino's mass from Planck length
• Classical axisymmetric gravity in real Ashtekar variables
• On the Nature of Black Holes in Loop Quantum Gravity
• Angular Momentum in Loop Quantum Gravity
• Modelling black holes with angular momentum in loop quantum gravity
• On the fundamental length of quantum geometry and the black hole entropy