Entropy of black holes in $$\mathcal {N}=2$$N=2 supergravity

Abstract

Using the formalism of isolated horizons, we construct space of solutions of asymptotically flat extremal black holes in $$\mathcal {N}=2$$ pure supergravity in 4 dimensions. We prove that the laws of black hole mechanics hold for these black holes. Further, restricting to constant area phase space, we show that the spherical horizons admit a Chern–Simons theory. Standard way of quantizing this topological theory and counting states confirms that entropy is indeed proportional to the area of horizon.