Report
The Stability of Relativistic Fluids in Linearly Expanding Cosmologies
| العنوان: | The Stability of Relativistic Fluids in Linearly Expanding Cosmologies |
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| المؤلفون: | Fajman, David, Ofner, Maximilian, Oliynyk, Todd A., Wyatt, Zoe |
| المصدر: | Int. Math. Res. Not. 2024 (2024), 4328-4383 |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics General Relativity and Quantum Cosmology |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, General Relativity and Quantum Cosmology, 35Q75, 35Q31, 83C05, 83F05 |
| الوصف: | In this paper we study cosmological solutions to the Einstein--Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly expanding cosmological spacetimes with a linear equation of state $p=K \rho$ for the parameter values $K \in (0,1/3)$. This removes the restriction to irrotational perturbations in earlier work, and relies on a novel transformation of the fluid variables that is well-adapted to Fuchsian methods. We then apply this new transformation to show the global regularity and stability of the Milne spacetime under the coupled Einstein--Euler equations, again with a linear equation of state $p=K \rho$, $K \in (0,1/3)$. Our proof requires a correction mechanism to account for the spatially curved geometry. In total, this is indicative that structure formation in cosmological fluid-filled spacetimes requires an epoch of decelerated expansion. Comment: 35 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1093/imrn/rnad241 |
| URL الوصول: | http://arxiv.org/abs/2301.11191 |
| رقم الانضمام: | edsarx.2301.11191 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1093/imrn/rnad241 |
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