Black Holes: Fermions at the Extremal Limit?

I present exact results matching Kerr-Newman Black Hole thermodynamics in the extremal limit to the two-dimensional Fermi Gas. Two dimensions are consistent with the membrane paradigm of black holes. Key in the analysis is the thermodynamic Riemannian curvature scalar $R$, negative for most ordinary thermodynamic systems, including those near the critical point, but mostly positive for the Kerr-Newman Black Hole and the Fermi Gas.