The reverse Burnett conjecture for null dusts
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916788840693760 |
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| author | Touati, Arthur |
| author_facet | Touati, Arthur |
| contents | Given a regular solution $\mathbf{g}_0$ of the Einstein-null dusts system without restriction on the number of dusts, we construct families of solutions $(\mathbf{g}_λ)_{λ\in(0,1]}$ of the Einstein vacuum equations such that $\mathbf{g}_λ-\mathbf{g}_0$ and $\partial(\mathbf{g}_λ-\mathbf{g}_0)$ converges respectively strongly and weakly to 0 when $λ\to0$. Our construction, based on a multiphase geometric optics ansatz, thus extends the validity of the reverse Burnett conjecture without symmetry to a large class of massless kinetic spacetimes. In order to deal with the finite but arbitrary number of direction of oscillations we work in a generalised wave gauge and control precisely the self-interaction of each wave but also the interaction of waves propagating in different null directions, relying crucially on the non-linear structure of the Einstein vacuum equations. We also provide the construction of oscillating initial data solving the vacuum constraint equations and which are consistent with the spacetime ansatz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17530 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The reverse Burnett conjecture for null dusts Touati, Arthur Analysis of PDEs General Relativity and Quantum Cosmology Given a regular solution $\mathbf{g}_0$ of the Einstein-null dusts system without restriction on the number of dusts, we construct families of solutions $(\mathbf{g}_λ)_{λ\in(0,1]}$ of the Einstein vacuum equations such that $\mathbf{g}_λ-\mathbf{g}_0$ and $\partial(\mathbf{g}_λ-\mathbf{g}_0)$ converges respectively strongly and weakly to 0 when $λ\to0$. Our construction, based on a multiphase geometric optics ansatz, thus extends the validity of the reverse Burnett conjecture without symmetry to a large class of massless kinetic spacetimes. In order to deal with the finite but arbitrary number of direction of oscillations we work in a generalised wave gauge and control precisely the self-interaction of each wave but also the interaction of waves propagating in different null directions, relying crucially on the non-linear structure of the Einstein vacuum equations. We also provide the construction of oscillating initial data solving the vacuum constraint equations and which are consistent with the spacetime ansatz. |
| title | The reverse Burnett conjecture for null dusts |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2402.17530 |