Wavy Strings: Black or Bright?

TL;DR

This work investigates time-dependent hair on black objects generated by the Garfinkle-Vachaspati method. It proves a general theorem that GV-induced waves do not affect any scalar curvature or matter invariants, but their presence can still reveal pathologies through tidal forces, with higher multipoles (l≥1) producing null singularities on the horizon in a concrete 5D black-string example. It further identifies a special class of longitudinal (l=0) waves for which the horizon can be analytic and regular, offering rare examples of time-dependent hair that do not spoil horizon regularity. Collectively, the results clarify the limitations of using curvature invariants to detect GV hair, delineate when wavy strings remain black-string-like, and guide future exploration of non-stationary hair in higher-dimensional and string-theoretic contexts.

Abstract

Recent developments in string theory have brought forth a considerable interest in time-dependent hair on extended objects. This novel new hair is typically characterized by a wave profile along the horizon and angular momentum quantum numbers $l,m$ in the transverse space. In this work, we present an extensive treatment of such oscillating black objects, focusing on their geometric properties. We first give a theorem of purely geometric nature, stating that such wavy hair cannot be detected by any scalar invariant built out of the curvature and/or matter fields. However, we show that the tidal forces detected by an infalling observer diverge at the `horizon' of a black string superposed with a vibration in any mode with $l \ge 1$. The same argument applied to longitudinal ($l=0$) waves detects only finite tidal forces. We also provide an example with a manifestly smooth metric, proving that at least a certain class of these longitudinal waves have regular horizons.