Presence of exotic matter in Levia–Civita and cosmic string solutions

This paper explores the cylindrically symmetric solutions within the framework of modified [Formula: see text] theories of gravity, where [Formula: see text] is the Ricci scalar. This study focuses on analyzing the cylindrical solutions within realistic space-time regions and investigates three distinct cases of exact solutions derived from the field equations of the [Formula: see text] theory of gravity. For our current work, we examine the well-known Levi-Civita and cosmic string solutions in [Formula: see text] modified theory of gravity. Furthermore, we also discuss the energy conditions for considered cases. Notably, a violation of null energy conditions is observed, suggesting the potential existence of cylindrical wormholes. The findings contribute to the understanding of modified [Formula: see text] theories of gravity, providing valuable insights into the nature of cylindrically symmetric solutions and their implications in theoretical physics.