Wavy strings: Black or bright?

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 ≥ 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.

How hairy can a black ring be?

“…The similarity with the results of [15,16] suggests that there will be a parallelly-propagated curvature singularity although we have not proved this. Although C 2 is the minimum degree of differentiability usually demanded of spacetime, one might ask whether the metric can be extended through a horizon of lower differentiability, such as the C 0 horizon of [14], as would be required to assign an area to the horizon.…”

“…After the waves are added, the metric is still continuous at the horizon and all scalar curvature invariants remain finite [14]. Nevertheless, it turns out that there is a curvature singularity at the horizon because certain curvature components in a basis parallelly propagated along a geodesic will diverge there [15,16]. More physically, a freely falling observer will experience infinite tidal forces.…”

String theory and the classical stability of plane waves

“…3 It is amusing to note that one encounters these "pp-curvature singularities" in the solutions describing ppwaves on fundamental strings [42,43,44,45], and also in non-dilatonic "brane-wave" solutions of ten-and elevendimensional supergravity [46]. In that case, even the exact plane waves give rise to such curvature singularities at the would-be horizon of the brane.…”

Statistical effects and the black-hole–D-brane correspondence

“…For the purposes of this discussion, let us impose the boundary conditions that K and A i are bounded near infinity so that we do not modify the asymptotic structure of the spacetime. While the general form of these equations has not yet been derived, one expects that the rough picture developed in [21,22] will continue to hold with the fields K, A i , and A a being entirely determined by the various multipole moments of the charge distributions and having the property that, whenever any of the dipole or higher moments is nonzero, the solution is singular on the horizon. This was shown in [14,22] to be precisely true of the field K and a short calculation based on the result of [22] shows that, at least for the case studied there, this singularity is 'strong' in the sense that both the once and twice integrated curvatures also diverge at the horizon.…”