Black Strings and Classical Hair

TL;DR

This paper investigates the near-horizon geometry of black strings with traveling waves, revealing that the horizon becomes singular in the presence of waves, contrary to previous assumptions of smoothness.

Contribution

It demonstrates that black string horizons are singular when traveling waves are present, challenging prior beliefs about their smoothness.

Findings

Horizon geometry is not smooth with traveling waves.

Black string horizons become singular due to waves.

Results apply to both five and six dimensional black strings.

Abstract

We examine the geometry near the event horizon of a family of black string solutions with traveling waves. It has previously been shown that the metric is continuous there. Contrary to expectations, we find that the geometry is not smooth, and the horizon becomes singular whenever a wave is present. Both five dimensional and six dimensional black strings are considered with similar results.