A study of Morris–Thorne wormhole in Einstein–Cartan theory

Abstract

This paper focuses on the Einstein–Cartan theory, an extension of general relativity that incorporates a torsion tensor into spacetime. The differential form technique is employed to analyze the Einstein–Cartan theory, which replaces tensors with tetrads. A tetrad formalism, specifically the Newman–Penrose–Jogia–Griffiths formalism, is used to study the field equations. Also, the energy–momentum tensor is determined, considering a Weyssenhoff fluid with anisotropic matter. The spin density is derived in terms of the redshift function. Additionally, our findings demonstrate that the radial sound speed within the wormhole throat exceeds the speed of light, suggesting the existence of superluminal matter, while the tangential sound speed indicates near-light-speed propagation, particularly within the throat, emphasizing the significance of exotic matter in comprehending wormhole properties. The results also extend to examining the energy conditions at the throat of a Morris–Thorne wormhole, shedding light on the properties of wormholes within the context of the Einstein–Cartan theory, including the energy conditions at the throat.