Black Rings, Boosted Strings and Gregory-Laflamme

Abstract

We investigate the Gregory-Laflamme instability for black strings carrying KK-momentum along the internal direction. We demonstrate a simple kinematical relation between the thresholds of the classical instability for the boosted and static black strings. We also find that Sorkin's critical dimension depends on the internal velocity and in fact disappears for sufficiently large boosts. Our analysis implies the existence of an analogous instability for the five-dimensional black ring of Emparan and Reall. We also use our results for boosted black strings to construct a simple model of the black ring and argue that such rings exist in any number of space-time dimensions.

Figures (6)

• Figure 1: Unstable frequencies and wavenumbers for the static black string.
• Figure 2: Frequencies $\tilde{\Omega}(\tilde{k})$ and $\tilde{\omega}(\tilde{k})$ leading to instabilities, as observed in static ($\tilde{t},\tilde{z}$) frame, for $n=1$.
• Figure 3: Plot of physical frequencies $\Omega(k)$ and $\omega(k)$ leading to boosted string instabilities for fixed horizon size, at various boost velocities and with $n=1$.
• Figure 4: Comparison of the threshold wave-number calculated numerically (\ref{['rminbs']}) (blue, solid) to that predicted by global entropy considerations (\ref{['eq:prediction2']}) (red, dashed) for $D=5,7,10,20$
• Figure 5: The critical boost at which nonuniform black strings become stable in various dimensions. (The curve is simply a guide to the eye.)