Internal Structure of Black Holes

TL;DR

This paper explores the internal structure of extremal dyonic black holes in string theory, proposing a non-perturbative degeneracy formula that aligns with black hole entropy and suggests a rich hair structure leading to an effective string description.

Contribution

It introduces a simple, parameter-free expression for the non-perturbative degeneracy of extremal black holes, linking microstates to an effective string theory framework.

Findings

Degeneracy formula reproduces Bekenstein-Hawking entropy in large-area limit

Black holes support extensive hair, enabling microstate counting

Effective string theory describes the microstates of these black holes

Abstract

We present a number of qualitative arguments which strongly suggest that extremal dyonic black holes in the 4--dimensional low energy, classical field theory limit of toroidally compactified heterotic string theory represent largely degenerate classes of states in the quantum theory. We propose a simple expression for the full non--perturbative degeneracy, which contains no free continuous parameters and reproduces the Bekenstein-Hawking $S={A\over 4G_N}$ in the large-area limit (with the ${1\over 4}$ arising from microphysics). We sketch the elements of a physical picture leading to this expression: the holes support much hair, such that in counting it we are led to an effective string theory, and a matching condition whose solutions give the degeneracy.