Black hole state counting in loop quantum gravity

TL;DR

This paper compares different methods of counting black hole microstates in loop quantum gravity, clarifies the role of quantum constraints, and extends the analysis from U(1) to SU(2) formulations.

Contribution

It provides a detailed comparison of state counting methods in loop quantum gravity and clarifies the significance of various quantum labels and constraints.

Findings

Counting all allowed j,m labels differs from counting only m labels.

Constraints on m are clarified and related to flux quantum numbers.

Configurations with |m|=j are significant mainly for large areas.

Abstract

The two ways of counting microscopic states of black holes in the U(1) formulation of loop quantum gravity, one counting all allowed spin network labels j,m and the other only m labels, are discussed in some detail. The constraints on m are clarified and the map between the flux quantum numbers and m discussed. Configurations with |m|=j, which are sometimes sought after, are shown to be important only when large areas are involved. The discussion is extended to the SU(2) formulation.