Rotating nonuniform black string solutions

TL;DR

The paper extends the study of Gregory-Laflamme stability to rotating uniform black strings with equal angular momenta in even dimensions, showing the instability persists up to extremality for $6 \le D \le 14$, and uses this framework to construct rotating nonuniform black strings in $D=6$ as well as charged rotating UBS in heterotic string theory via solution-generating techniques. It develops a robust numerical approach to solve the five coupled PDEs governing the rotating nonuniform strings, revealing a critical temperature $T_*$ that marks a topology-changing transition in the rotating sector and demonstrating backbending in tension. The work provides detailed thermodynamic analyses, horizon and ergoregion characterizations, and global charge relations, highlighting how rotation interplays with stability and phase structure and offering a holographic perspective on the phase diagram of higher-dimensional black objects. Overall, these results illuminate the rich landscape of rotating black strings and their connections to GM stability, topology-changing transitions, and string-theoretic charged generalizations.

Abstract

We explore via linearized perturbation theory the Gregory-Laflamme instability of rotating black strings with equal magnitude angular momenta. Our results indicate that the Gregory-Laflamme instability persists up to extremality for all even dimensions between six and fourteen. We construct rotating nonuniform black strings with two equal magnitude angular momenta in six dimensions. We see a first indication for the occurrence of a topology changing transition, associated with such rotating nonuniform black strings. Charged nonuniform black string configurations in heterotic string theory are also constructed by employing a solution generation technique.

Figures (11)

• Figure 1: The dimensionless quantity $a^2/ \left( p(D) M^{\frac{2}{D-4}} \right)$ is shown as a measure of the rotation of the uniform black strings at constant temperature $2 \pi T_{H}=1$ in $D$ even dimensions, $6 \le D \le 14$, versus the wavenumber $k$ of the zeromode fluctuation.
• Figure 2: Left: The relation between the scaled mass $M_s$ and scaled angular momentum $J_s$ for fixed critical length of the extra dimension $L$ is shown for rotating solutions in $D$ even dimensions, $6 \le D \le 14$. Both $M_s$ and $J_s$ are equipped with suitable powers and normalizations. $L_0$ represents the value where the instability of the static uniform black string occurs. Right: The ratio betwen the wavelength estimate $k^{(est)}$ and the value of $k$ found numerically is plotted at constant temperature $2 \pi T_{H}=1$ as function of the dimensionless quantity $a^2/ \left( p(D) M^{\frac{2}{D-4}} \right)$.
• Figure 3: The metric functions $A$, $B$, $C$, $G$ and $W$ of the $D=6$ rotating nonuniform black string solution with temperature parameter $d_0=0.6$ and horizon angular velocity $\Omega_H=0.25$ (left column) and $\Omega_H=0.202$ (right column) are shown as functions of the compactified radial coordinate $\rho$, and the coordinate $\zeta$ of the compact direction. Note that the horizon is located at $\rho=0$.
• Figure 3: continued.
• Figure 4: The spatial embedding of the horizon of $D=6$ rotating black string solutions is shown for a sequence of solutions with fixed temperature parameter $d_0=0.6$ and varying horizon angular velocity $\Omega_{H}$: $\Omega_{H}=0.34908$ (upper row), $\Omega_{H}=0.25$ (second row), $\Omega_{H}=0.212$ (third row) and $\Omega_{H}=0.202$ (lower row), $\lambda$ specifies the increasing nonuniformity of the solutions. Left column: side view, right column: view in $z$ direction. ($r_0 =1$, $L=L^{\rm crit}=4.9516$.)