Quasinormal Modes of pp-Wave Spacetimes and Zero Temperature Dissipation

Abstract

We compute the quasinormal mode spectrum of scalar perturbations on Kaigorodov pp-wave spacetimes, the horizonless gravity duals of zero temperature null fluids. The pp-wave deformation promotes the Poincar\'e horizon at $r=0$ to an irregular singular point of rank $(d+2)/2$, which acts as a geometric absorber for ingoing waves: rank~$0$ corresponds to thermal dissipation, rank~$1$ to quantum-critical (extremal black hole), and rank~$\geq 2$ to gapped, horizonless dissipation. For $d=2$ (extremal BTZ) the radial equation reduces to the Whittaker equation with exact non-dissipative spectrum $\mathrm{Im}(\omega)=0$; for $d \geq 3$ all modes satisfy $\mathrm{Im}(\omega_n) < 0$, establishing zero temperature dissipation without horizon or entropy. At zeroth order the radial equation becomes Bessel's equation of order $\mu=d/(d+2)$, proving all scalar QNMs are gapped. Numerical spectra for $d=3,4,5$ yield a discrete dissipative tower and confirm linear stability.