Quasinormal Modes, the Area Spectrum, and Black Hole Entropy

The results of loop quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labeled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole to fix this parameter in a new way. As a result we arrive at the Bekenstein-Hawking expression of $A/4l_P^2$ for the entropy of a black hole and in addition see an indication that the appropriate gauge group of quantum gravity is SO(3) and not its covering group SU(2).

Figure 1

In loop quantum gravity the area of a surface is quantized.If a surface intersects a spin network edge with label $j$ it acquires an area of $8\pi \gamma l_P^2\sqrt{j(j+1)}$. The parameter $\gamma$ is called the Immirzi parameter.

Figure 2

This figure shows the first 124 quasinormal mode frequencies of a Schwarzschild black hole.