Black Hole Entropy Function, Attractors and Precision Counting of Microstates

TL;DR

This paper reviews recent advances in understanding extremal black hole entropy through the entropy function formalism and presents precise microscopic counting of BPS dyon states, comparing statistical and black hole entropies.

Contribution

It introduces a detailed analysis of the attractor mechanism and provides exact microstate degeneracy calculations for quarter BPS dyons in N=4 theories, linking microscopic and macroscopic entropy.

Findings

Agreement between microscopic and macroscopic entropy expansions

Inclusion of multi-centered black hole contributions

Refined understanding of attractor mechanism in extremal black holes

Abstract

In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N=4 supersymmetric string theories, and compare the statistical entropy of these dyons, expanded in inverse powers of electric and magnetic charges, with a similar expansion of the corresponding black hole entropy. This comparison is extended to include the contribution to the entropy from multi-centered black holes as well.