Cylindrically symmetric fluid in unimodular $f(R)$ gravity

In this paper, we examine static cylindrical symmetric fluid in unimodular $f(R)$ gravity. Unimodularity for cylindrical symmetric spacetime geometry is ensured with a coordinate transformation by using tetrad formalism. Field equation solutions for given matter and the spacetime are obtained. Resource of cosmic matter is discussed by using Equation of State (EoS) and energy conditions. We investigate weak and strong energy conditions in unimodular $f(R)$ gravity context with the help of Raychaudhuri equations. Obtained results show that fluids which violate the energy conditions cause the proposed unimodular and cylindrical symmetric wormholes, but this kind of wormholes do not satisfy traversability conditions. Furthermore, the obtained solutions indicate that $\omega $ coefficient in EoS must have the condition $\omega \neq -1$ for physically meaningful fluids. It is discussed whether the result is compatible with the unimodular gravitation theories.