Entropy of Black Holes in N=2 Supergravity

TL;DR

This paper constructs the solution space of extremal black holes in N=2 supergravity, proves black hole laws, and confirms that horizon entropy is proportional to area via Chern-Simons theory quantization.

Contribution

It introduces a novel approach to analyzing extremal black holes in N=2 supergravity using isolated horizon formalism and topological quantum field theory methods.

Findings

Entropy proportional to horizon area confirmed

Chern-Simons theory describes horizon degrees of freedom

Laws of black hole mechanics established

Abstract

Using the techniques of isolated horizon formalism, we construct the space of solutions of asymptotically flat extremal black holes in N=2 pure supergravity in 4 dimensions. We prove the laws of black hole mechanics. Further, restricting to constant area phase space, we show that the spherical horizons admits a U(1) Chern- Simons theory. Standard way of quantizing this topological theory and counting states confirms that entropy is indeed proportional to the area of horizon.