Abstract
An exact solution pertaining to the existence of cosmic strings has been discussed for a cylindrically symmetric $f(\mathcal{G},T)$ gravity model, with $\mathcal{G}$ being the Gauss-Bonnet invariant and $T$ the trace of energy momentum tensor. This solution corresponds to the generalised vacuum Levi-Civita’s metric in general relativity. Exclusive expressions for the energy density and pressure terms along with their corresponding null energy constraints have been worked out and analyzed graphically. It has been shown that the energy density remains positive and the null energy conditions are met largely for some particular choices of the parametric terms appearing in the model. However, certain violation of these energy constraints under specific circumstances hints the existence of cylindrical wormholes. Moreover, if the coupling constant of the Gauss-Bonnet invariant is set to null, Levi-Civita vacuum solution in general relativity is recovered.
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