Static plane symmetric solutions in $f(Q)$ gravity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911668384038912 |
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| author | Long, Jun-Qin Lin, Rui-Hui Zhai, Xiang-Hua |
| author_facet | Long, Jun-Qin Lin, Rui-Hui Zhai, Xiang-Hua |
| contents | We systematically investigate static plane symmetric configurations in $f(Q)$ gravity. For vacuum regions, we discuss the constancy of the nonmetricity scalar $Q$ and derive general vacuum solutions, which correspond effectively to Taub-(anti) de Sitter spacetimes with a cosmological constant determined by the specific $f(Q)$ model. By matching a singular thin shell source to the vacuum solutions, we relate the shell's energy density and pressure to the integration constants of the exterior geometry. We also examine a finite-thickness slab as another matter source supporting the vacuum solution. Through numerical analysis of a quadratic model $f(Q)=Q+αQ^2$ with isotropic matter, we show that the maximum pressure inside the slab generally does not coincide with the geometric center. Moreover, a negative $α$ with larger magnitude leads to higher internal pressure and a thicker slab, while models with positive $α$ are incompatible with a self-gravitating slab of positive pressure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Static plane symmetric solutions in $f(Q)$ gravity Long, Jun-Qin Lin, Rui-Hui Zhai, Xiang-Hua General Relativity and Quantum Cosmology We systematically investigate static plane symmetric configurations in $f(Q)$ gravity. For vacuum regions, we discuss the constancy of the nonmetricity scalar $Q$ and derive general vacuum solutions, which correspond effectively to Taub-(anti) de Sitter spacetimes with a cosmological constant determined by the specific $f(Q)$ model. By matching a singular thin shell source to the vacuum solutions, we relate the shell's energy density and pressure to the integration constants of the exterior geometry. We also examine a finite-thickness slab as another matter source supporting the vacuum solution. Through numerical analysis of a quadratic model $f(Q)=Q+αQ^2$ with isotropic matter, we show that the maximum pressure inside the slab generally does not coincide with the geometric center. Moreover, a negative $α$ with larger magnitude leads to higher internal pressure and a thicker slab, while models with positive $α$ are incompatible with a self-gravitating slab of positive pressure. |
| title | Static plane symmetric solutions in $f(Q)$ gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.19207 |