Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors
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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_ | 1866913977738461184 |
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| author | Guo, Yuyang Hu, Jun Lin, Ting |
| author_facet | Guo, Yuyang Hu, Jun Lin, Ting |
| contents | The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper proposes a new formulation that treats the linearized Einstein-Bianchi system (near the trivial Minkowski metric) as the Hodge wave equation associated with the conformal Hessian complex. To discretize this equation, a conforming finite element conformal Hessian complex that preserves symmetry and traceless-ness simultaneously is constructed on general three-dimensional tetrahedral grids, and its exactness is proven. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors Guo, Yuyang Hu, Jun Lin, Ting Numerical Analysis General Relativity and Quantum Cosmology 65N30 The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper proposes a new formulation that treats the linearized Einstein-Bianchi system (near the trivial Minkowski metric) as the Hodge wave equation associated with the conformal Hessian complex. To discretize this equation, a conforming finite element conformal Hessian complex that preserves symmetry and traceless-ness simultaneously is constructed on general three-dimensional tetrahedral grids, and its exactness is proven. |
| title | Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors |
| topic | Numerical Analysis General Relativity and Quantum Cosmology 65N30 |
| url | https://arxiv.org/abs/2508.04560 |