After the Fluid: Subexponential Decay in AdS$_4$

We study the late-time behaviour of nonlinear perturbations of Schwarzschild-AdS$_4$ black branes and show that real-analytic initial data generically enter a regime controlled by the large-$k$ tail of the quasinormal mode spectrum $\{\omega_{k\,n}\}$. Using the asymptotic scaling $\mathrm{Im}\,\omega_{k\,n} \sim k^{-1/5}$ of the planar AdS$_4$ black brane, we derive a universal prediction that boundary observables decay in a stretched-exponential manner, specifically as $\exp(-c\, t^{5/6})$ up to a mild polynomial prefactor. Fully nonlinear numerical evolutions employing Fourier spectral and discontinuous Galerkin methods confirm this behaviour for small black holes and show consistent scaling - after suppressing long-lived low-$k$ modes - for larger ones. These results indicate that stretched-exponential decay with exponent $5/6$ is a robust feature of AdS$_4$ gravitational dynamics with real-analytic data, arising from geometric-optics physics rather than hydrodynamic modes.