Classification of static cylindrically symmetric spacetimes in f(R) theory of gravity by conformal motions with perfect fluid matter

Abstract Assuming the source of energy momentum tensor as perfect fluid, a classification of static cylindrically symmetric spacetimes in f(R) theory of gravity by conformal vector fields (CVFs) is presented. For the classification purpose, we put different conditions on metric coefficients to obtain solutions in f(R) theory of gravity. By means of some algebraic and direct integration techniques, it is shown that the dimension of CVFs for the considered spacetimes turns out to be 4, 5, or 15