Counting States of Black Strings with Traveling Waves II

TL;DR

The paper demonstrates that extremal black strings with traveling waves—including angular-momentum-carrying waves in six dimensions and linear-momentum-carrying waves in five dimensions—possess homogeneous horizons whose areas reproduce the Bekenstein-Hawking entropy. It achieves this by deriving near-horizon geometries, horizon areas, and then matching these gravitational entropies to microscopic BPS-state counts in the weak-coupling D-brane description using a mesoscopic segment approach. The results show a full quantitative agreement between macroscopic gravity and microscopic string states for inhomogeneous momentum distributions, reinforcing the entropy correspondence in more general dynamical settings. The discussion clarifies how a local, segment-level counting coexists with global horizon structure and explores implications for rotating black holes, highlighting when spin versus gyration contributions maximize entropy under physical constraints.

Abstract

We extend our recent analysis of the entropy of extremal black strings with traveling waves. We previously considered waves carrying linear momentum on black strings in six dimensions. Here we study waves carrying angular momentum on these strings, and also waves carrying linear momentum on black strings in five dimensions. In both cases, we show that the horizon remains homogeneous and compute its area. We also count the number of BPS states at weak string coupling with the same distribution of linear and angular momentum, and find complete agreement with the black string entropy.