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arXiv · 2505.22590

Local well-posedness of the initial value problem in Einstein-Cartan theory

Paulo Luz·Filipe C. Mena
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Abstract

We study the initial value problem in Einstein-Cartan theory which includes torsion and, therefore, a non-symmetric connection on the spacetime manifold. Generalizing the path of a classical theorem by Choquet-Bruhat and York for the Einstein equations, we use a $n+1$ splitting of the manifold and compute the evolution and constraint equations for the Einstein-Cartan system. In the process, we derive the Gauss-Codazzi-Ricci equations including torsion. We prove that the constraint equations are preserved during evolution. Imposing a generalized harmonic gauge, it is shown that the evolution equations can be cast as a quasilinear system in a Cauchy regular form with a characteristic determinant having a non-trivial multiplicity of characteristics. Using the Leray-Ohya theory for non-strictly hyperbolic systems we then establish the local geometric well-posedness of the Cauchy problem, for sufficiently regular initial data. For vanishing torsion we recover the classical results for the Einstein equations.

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Paulo Luz, Filipe C. Mena. 2025-05-28. Local well-posedness of the initial value problem in Einstein-Cartan theory. https://arxiv.org/abs/2505.22590

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