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arXiv · 2508.04560

Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors

Yuyang Guo·Jun Hu·Ting Lin
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Abstract

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.

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Yuyang Guo, Jun Hu, Ting Lin. 2025-08-06. Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors. https://arxiv.org/abs/2508.04560

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