Consistent solution of Einstein-Cartan equations with torsion outside matter

TL;DR

This paper explores solutions to Einstein-Cartan equations with torsion outside matter, revealing a non-spherical, torsion-influenced solution that extends classical black hole models and discusses implications for cosmology and wormholes.

Contribution

It derives a new outside-matter solution with torsion in Einstein-Cartan theory, demonstrating its uniqueness and non-spherical nature, and explores its cosmological and wormhole properties.

Findings

A second solution outside matter with torsion is found beyond Schwarzschild.

The solution is non-spherical and uniquely determined by consistency conditions.

Wormhole configurations are identified under specific parameters.

Abstract

The Einstein-Cartan equations 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-Lama\^itre-Robertson-Walker cosmoses. 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.