Electromagnetic Field and Cylindrical Compact Objects in Modified Gravity

In this paper, we have investigated the role of different fluid parameters particularly electromagnetic field and $f(R)$ corrections on the evolution of cylindrical compact object. We have explored the modified field equations, kinematical quantities and dynamical equations. An expression for the mass function has been found in comparison with the Misner-Sharp formalism in modified gravity, after which different mass radius diagrams are drawn. The coupled dynamical transport equation have been formulated to discuss the role of thermoinertial effects on the inertial mass density of the cylindrical relativistic interior. Finally, we have presented a framework, according to which all possible solutions of the metric $f(R)$-Maxwell field equations coupled with static fluid can be written through set of scalar functions. It is found that modified gravity induced by Lagrangians $f(R)=\alpha R^2,~f(R)=\alpha R^2-\beta R$ and $f(R)=\frac{\alpha R^2-\beta R}{1+\gamma R}$ are likely to host more massive cylindrical compact objects with smaller radii as compared to GR.