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Consistent solution of Einstein–Cartanequations with torsion outside matter
Classical and Quantum Gravity  (IF3.528),  Pub Date : 2021-09-24, DOI: 10.1088/1361-6382/ac2417
Klaus Morawetz

The Einstein–Cartanequations in first-order action of torsion are considered. From Belinfante–Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion is given by the spin which leads to an extended Oppenhaimer–Volkov equation. Outside matter a second solution is found besides the torsion-free Schwarzschild one with the torsion completely determined by the metric and vice versa. This solution is shown to be of non-spherical origin and its uniqueness with respect to the consistence is demonstrated. Unusual properties are discussed in different coordinate systems where the cosmological constant assumes the role of the Friedman parameter in Friedman–Lamatre–Robertson–Walkercosmoses. Parameters are specified where wormholes are possible. Transformations are presented to explore and map regions of expanding and contracting universes to the form of static metrics. The autoparallel equations are solved exactly and compared with geodesic motion. The Weyl tensor reveals that the here found solution is of Petrov-D type.