A study of Levi-Civita’s cylindrical solutions in f ( R , φ) gravity

This manuscript is dedicated to discussing the cylindrical symmetric solutions in a well-known gravity, namely the f ( R , φ) theory of gravity, where R stands for Ricci scalar and φ represents the scalar potential. For our current study, f ( R , φ) = ( 1 + ξ λ 2 φ 2 ) R gravity model is used to find the exact solutions of field equations. Furthermore, a well-known Levi-Civita solution by considering some parameters has been investigated. We exclusively worked out the expressions of density and pressure terms and analyzed them graphically. Energy conditions especially null energy conditions are examined while discussing the exact solutions of all these cases. It is concluded that the null energy conditions are violated for some specific regions, which is an indication of the existence of cylindrical wormholes. The charming and fascinating feature of this task is two-dimensional and three-dimensional investigation.

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