Stability of fluids in spacetimes with decelerated expansion
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912199344128000 |
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| author | Fajman, David Ofner, Maximilian Oliynyk, Todd Wyatt, Zoe |
| author_facet | Fajman, David Ofner, Maximilian Oliynyk, Todd Wyatt, Zoe |
| contents | We prove the nonlinear stability of homogeneous barotropic perfect fluid solutions in fixed cosmological spacetimes undergoing decelerated expansion. The results hold provided a specific inequality between the speed of sound of the fluid and the expansion rate of spacetime is valid. Numerical studies in our earlier complementary paper provide strong evidence that the aforementioned condition is sharp, i.e. that instabilities occur when the inequality is violated. In this regard, our present result covers the regime of slowest possible expansion which allows for fluids to stabilize, depending on their speed of sound. Our proof relies on an energy functional which is universal in the sense that it also applies to the case of linear expansion and enables a significantly simplified proof of bounds for fluids on linearly expanding spacetimes. Finally, we consider the special cases of dust and radiation fluids in the decelerated regime and prove shock formation for arbitrarily small perturbations of homogeneous solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_12798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of fluids in spacetimes with decelerated expansion Fajman, David Ofner, Maximilian Oliynyk, Todd Wyatt, Zoe General Relativity and Quantum Cosmology Mathematical Physics 35Q75, 83C05, 35B35 We prove the nonlinear stability of homogeneous barotropic perfect fluid solutions in fixed cosmological spacetimes undergoing decelerated expansion. The results hold provided a specific inequality between the speed of sound of the fluid and the expansion rate of spacetime is valid. Numerical studies in our earlier complementary paper provide strong evidence that the aforementioned condition is sharp, i.e. that instabilities occur when the inequality is violated. In this regard, our present result covers the regime of slowest possible expansion which allows for fluids to stabilize, depending on their speed of sound. Our proof relies on an energy functional which is universal in the sense that it also applies to the case of linear expansion and enables a significantly simplified proof of bounds for fluids on linearly expanding spacetimes. Finally, we consider the special cases of dust and radiation fluids in the decelerated regime and prove shock formation for arbitrarily small perturbations of homogeneous solutions. |
| title | Stability of fluids in spacetimes with decelerated expansion |
| topic | General Relativity and Quantum Cosmology Mathematical Physics 35Q75, 83C05, 35B35 |
| url | https://arxiv.org/abs/2501.12798 |