Gyrating Strings: A new instability of black strings?

TL;DR

This work identifies a new instability mechanism for near-extremal spinning D1-D5-P black strings, wherein excess angular momentum can preferentially transfer to gyration of the string, forming a rotating, helical configuration. By constructing gyrating solutions via Garfinkle-Vachaspati waves and decomposing charges into spin and gyrational parts, the authors derive an entropy function $S = 2 \pi \sqrt{ Q_1 Q_5 (N - N_{gyro}) - (J - J_{gyro})^2 }$ and show a critical threshold $J_{crit} = \frac{3 Q_1 Q_5}{2\sqrt{2}}$ above which the entropy is maximized by nonzero $J_{gyro}$, signaling a dynamical instability toward gyration. The analysis suggests two possible end states and argues that, in a non-BPS regime, this could provide a counterexample to the Gubser-Mitra conjecture, while noting that in the BPS limit the gyrational mode is a marginal bound state described by center-of-mass U(1) degrees of freedom. The results extend to D-brane bound states and offer a framework for further numerical and theoretical exploration of black string thermodynamics and stability.

Abstract

A thermodynamic argument is presented suggesting that near-extremal spinning D1-D5-P black strings become unstable when their angular momentum exceeds $J_{crit} = {3Q_1Q_5}/2\sqrt{2}$. In contrast, the dimensionally reduced black holes are thermodynamically stable. The proposed instability involves a phase in which the spin angular momentum above $J_{crit}$ is transferred to gyration of the string in space; i.e., to orbital angular momentum of parts of the string about the mean location in space. Thus the string becomes a rotating helical coil. We note that an instability of this form would yield a counter-example to the Gubser-Mitra conjecture, which proposes a particular link between dynamic black string instabilities and the thermodynamics of black strings. There may also be other instabilities associated with radiation modes of various fields. Our arguments also apply to the D-brane bound states associated with these black strings in weakly coupled string theory.