Non-Renormalization For Non-Supersymmetric Black Holes

We analyze large logarithmic corrections to 4D black hole entropy and relate them to the Weyl anomaly. We use duality to show that counter-terms in Einstein-Maxwell theory can be expressed in terms of geometry alone, with no dependence on matter terms. We analyze the two known $\mathcal{N} = 2$ supersymmetric invariants for various non-supersymmetric black holes and find that both reduce to the Euler invariant. The $c$-anomaly therefore vanishes in these theories and the coefficient of the large logarithms becomes topological. It is therefore independent of continuous black hole parameters, such as the mass, even far from extremality.