Charged Wormhole Solutions in Einstein-Cartan gravity

Abstract

Static solutions representing wormhole configurations in Einstein-Cartan theory ({\sf ECT}) in the presence of electric charge are obtained. The solutions are described by a constant redshift function with matter content consisting of a Weyssenhoff fluid along with an anisotropic matter and energy momentum tensor ({\sf EMT}) of the electric field which together generalize the anisotropic energy momentum tensor in Einstein-Maxwell theory in order to include the effects of the intrinsic angular momentum (spin) of the particles. Assuming the equation of state ({\sf EoS}) $p_r={\mathsf{w}}_1\rho$ and $p_t={\mathsf{w}}_2\rho$, we derive exact wormhole solutions satisfying weak and null energy conditions. Depending on the value of the spin square density at the wormhole throat these solutions can be asymptotically flat, de-Sitter or anti de-Sitter. Observational aspects of the wormhole solutions are also studied, using gravitational lensing effects. It is found that the throat can act as a photon sphere near which the light deflection angle has arbitrarily large values. Moreover, for a particular class of solutions, when ${\mathsf{w}}_1\to -{\mathsf{w}}_2$ the lensing features of the present model mimic those of the Ellis wormhole in the weak field limit.

18 pages, 6 figures

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