The extremely-tilted fluid regime near asymptotically Kasner big bang singularities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918350180843520 |
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| author | Beyer, Florian |
| author_facet | Beyer, Florian |
| contents | In this paper, we solve the relativistic Euler equations with a linear barotropic equation of state on a large class of background spacetimes with Kasner big bang asymptotics. Building on previous work in the asymptotically non-tilted regime, which applies when the speed of sound of the fluid is large in comparison to the Kasner exponents, we now consider the asymptotically extremely-tilted regime when the speed of sound is small. We solve the Cauchy problem for the Euler equations towards the big bang singularity and prove, without any symmetry assumptions or smallness conditions on the Cauchy data, that the solutions exist globally in time provided the mean curvature of the initial hypersurface is sufficiently large. Finally, we prove that the solutions exhibit the asymptotics expected from standard heuristic arguments in this regime; in particular, fluid particles are driven towards the speed of light in the direction of the largest Kasner exponent as the big bang singularity is approached. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19361 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The extremely-tilted fluid regime near asymptotically Kasner big bang singularities Beyer, Florian General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs In this paper, we solve the relativistic Euler equations with a linear barotropic equation of state on a large class of background spacetimes with Kasner big bang asymptotics. Building on previous work in the asymptotically non-tilted regime, which applies when the speed of sound of the fluid is large in comparison to the Kasner exponents, we now consider the asymptotically extremely-tilted regime when the speed of sound is small. We solve the Cauchy problem for the Euler equations towards the big bang singularity and prove, without any symmetry assumptions or smallness conditions on the Cauchy data, that the solutions exist globally in time provided the mean curvature of the initial hypersurface is sufficiently large. Finally, we prove that the solutions exhibit the asymptotics expected from standard heuristic arguments in this regime; in particular, fluid particles are driven towards the speed of light in the direction of the largest Kasner exponent as the big bang singularity is approached. |
| title | The extremely-tilted fluid regime near asymptotically Kasner big bang singularities |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2602.19361 |