Summary
The field equations of a specific gravitational Lagrangian, being quadratic in curvature and torsion, are solved by means of an ansatz for the curvature. The field equations are thereby reduced to a decoupled system of equations that determines the metric and the torsion. Up to this point, no symmetry conditions have been imposed on the fields. This system of equations is then solved for three special cases in each of which the torsion has a nonvanishing axial vector part.
Riassunto
Le equazioni di campo di una lagrangiana gravitazionale specifica, quadratica in curvatura e tensione, sono risolte per mezzo di un ansatz per la curvatura. Le equazioni di campo sono perciò ridotte ad un sistema disaccoppiato di equazioni che determina la metrica e la torsione. Sino a questo punto, nessuna condizione di simmetria è stata imposta sui campi. Questo sistema di equazioni è quindi risolto per tre casi speciali, in ciascuno dei quali la torsione ha una parte assiale vettoriale che non si annulla.
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Supported by a grant of the «Minister für Wissenschaft und Forschung des Landes Nordrhein-Westfalen».
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Lenzen, H.J. On space-time models with axial torsion: Some vacuum solutions of the Poincaré gauge field theory of gravity. Nuovo Cim B 82, 85–99 (1984). https://doi.org/10.1007/BF02723579
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DOI: https://doi.org/10.1007/BF02723579