String solutions in spherically-symmetric f(R) gravity vacuum

Dynamical evolution of the cosmic string in a spherically symmetric f(R) gravity vacuum is studied for a closed and straight string. We first set the background spacetime metric for a constant curvature scalar R = R-0, and obtain the Killing fields for it. Using the standard gauge coordinates and constraints for both closed and straight strings, we present the equation of motions and find the solutions of them. We then analyze the dynamics of the string by studying the behavior of the string radius and periastron radius, with respect to both proper time and azimuthal angle, for various values of f(R) functions. Consequently, we conclude that the value of f(R) dramatically affects the closed string collapse time and the straight string angular deviation.