Counting States of Black Strings with Traveling Waves

TL;DR

This work studies six-dimensional extremal black strings endowed with traveling waves, labeled by momentum-density profiles $p(u)$ and internal oscillations $f_i(u)$. The authors analyze the near-horizon geometry, establish horizon homogeneity, and compute the horizon area, showing that the Bekenstein-Hawking entropy $S_{BH} = A/(4 G_{10})$ matches the microscopic count of BPS string states at weak coupling with the same macroscopic momentum distribution under a slow-variation condition: $p^{3/2} \gg r_0^2|\dot p|$. They separate waves into longitudinal and internal types, proving that longitudinal waves determine the leading entropy via $S = \sqrt{2\pi Q_1 Q_5}\int_0^L \sqrt{p/\kappa^2}\,du$, while internal waves do not alter this leading term. The results extend the class of black string solutions for which microstate counting reproduces the macroscopic entropy and clarify that traveling waves act to constrain the momentum distribution rather than provide classical hair on the horizon.

Abstract

We consider a family of solutions to string theory which depend on arbitrary functions and contain regular event horizons. They describe six dimensional extremal black strings with traveling waves and have an inhomogeneous distribution of momentum along the string. The structure of these solutions near the horizon is studied and the horizon area computed. We also count the number of BPS string states at weak coupling whose macroscopic momentum distribution agrees with that of the black string. It is shown that the number of such states is given by the Bekenstein-Hawking entropy of the black string with traveling waves.