After the Fluid: Subexponential Decay in AdS$_4$
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| Format: | Preprint |
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2026
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| _version_ | 1866911696275111936 |
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| author | Crump, John R. V. Santos, Jorge E. |
| author_facet | Crump, John R. V. Santos, Jorge E. |
| contents | 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 $\{ω_{k\,n}\}$. Using the asymptotic scaling $\mathrm{Im}\,ω_{k\,n} \sim k^{-1/5}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | After the Fluid: Subexponential Decay in AdS$_4$ Crump, John R. V. Santos, Jorge E. High Energy Physics - Theory General Relativity and Quantum Cosmology 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 $\{ω_{k\,n}\}$. Using the asymptotic scaling $\mathrm{Im}\,ω_{k\,n} \sim k^{-1/5}$ 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. |
| title | After the Fluid: Subexponential Decay in AdS$_4$ |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.18978 |