Counting the microstates of a vacuum black ring

TL;DR

The work addresses the microscopic origin of the entropy of extremal vacuum black rings by identifying their near-horizon geometry with that of an extremal boosted Kerr string. Building on Horowitz–Roberts methods, it maps the ring charges to a boosted string and uses covering spaces and branch exchange to access a microstate-countable sector, yielding $S = 2\pi |J_2|$ for the ring. The analysis extends the ergo-branch KK black hole entropy framework to arbitrary angular momentum and provides a coherent microscopic counting that matches the Bekenstein–Hawking result through a sequence of dualities and coverings. While illuminating the role of near-horizon geometry in microstate counting, the approach also highlights limitations in distinguishing rings from boosted strings and in generalizing to non-ring black holes.

Abstract

The Bekenstein-Hawking entropy of an extremal vacuum black ring is derived from a microscopic counting of states. The entropy of extremal Kaluza-Klein black holes with ergospheres is also derived.