Canonical partition function of loop black holes

We compute the canonical partition function for quantum black holes in the approach of loop quantum gravity (LQG). We argue that any quantum theory of gravity in which the horizon area is built of noninteracting constituents cannot yield qualitative corrections to the Bekenstein-Hawking (B-H) area law, but corrections to the area law can arise as a consequence of additional constraints inducing interactions between the constituents. In LQG this is implemented by requiring spherical horizons. The canonical approach for LQG seemingly favors a logarithmic correction to the B-H law with a coefficient of $-\frac{1}{2}$. Our initial calculation of the partition function uses certain approximations that, we show, do not qualitatively affect the expression for the black hole entropy. We later discuss the quantitative corrections to these results when the simplifying approximations are relaxed and the full LQG spectrum is dealt with. We show how these corrections can be recovered to all orders in perturbation theory. However, the convergence properties of the perturbative series remain unknown for now.

Figure 1

Horizon punctured by the edges of a spin-network.