Consistent solution of Einstein–Cartan equations with torsion outside matter

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