Black hole state counting in loop quantum gravity

Understand

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.