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Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification

General Relativity and Quantum Cosmology 2025-07-03 v1 Mathematical Physics math.MP

Abstract

We present the complete set of covariant equations that govern the locally rotationally symmetric torsion spacetimes sourced by Weyssenhoff fluid in Einstein-Cartan-Sciama-Kibble gravity. Using these equations, we can explore in detail the peculiar relationship between conformal structure and torsion. We develop a comprehensive scheme to categorize these torsional spacetimes into distinct classes. We explicitly analyze the properties of each class and obtain novel analytical solutions to the gravitational field equations.

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Cite

@article{arxiv.2507.01840,
  title  = {Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification},
  author = {Ujjwal Agarwal and Sante Carloni},
  journal= {arXiv preprint arXiv:2507.01840},
  year   = {2025}
}

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19 pages