Impact of nonlinear electrodynamics on quasinormal modes of rotating black strings

Abstract

We study massless scalar perturbations of rotating anti-de Sitter black strings sourced by a power-Maxwell field with negative exponent $s$. The charge enters the metric function as $-Qr^{p}$ with $p=2/(1-2s)$, and the case $s=-1/2$ gives a linear term with an algebraic horizon. Since rotation is a local boost of the static string, the rotating spectrum follows exactly from the static one evaluated at a frequency-dependent momentum. We compute the spectrum with the Horowitz-Hubeny series, Chebyshev collocation and time-domain evolution, each implemented in two independent codes and checked against the planar Schwarzschild-AdS limit. The charge acts in two ways. At the reduced charge $\hat q_c=0.72626$ the least damped pair of modes meets on the imaginary axis, so more strongly charged strings ring down without oscillation, and at the endpoint of the branch the spectrum is exactly hypergeometric. At large transverse momentum the distance of the modes from the light cone grows as $k^{1/(1-4s)}$, replacing the $k^{-1/5}$ law of the neutral brane. Rotation continues the exceptional point into a line in the plane of charge and rotation, adds a purely damped axisymmetric tower, and never produces superradiant growth. A near-horizon estimate used earlier for this geometry misses all of these effects.