Ricci Solitons and String Cloud Spacetime in f(R)-gravity

The present study investigates the dynamics of a string cloud within the framework of f(R)-gravity theory. We analyze the properties of the string cloud spacetime governed by f(R) gravity, deriving expressions for the Ricci tensor, scalar curvature, and the equation of state. We find a delicate balance between the particle density \(\rho \) and string tension \(\lambda \) during the quintessence era. Additionally, employing the Ricci soliton as our metric, we determine conditions for the soliton’s behavior under different vector fields. We derive modified Poisson and Liouville equations and explore the formation of a black hole and trapped surfaces outside it in the context of a shrinking Ricci soliton within a string cloud spacetime under f(R)-gravity. Finally, by considering the gradient Ricci soliton, we establish conditions on the particle density \(\rho \) for the spacetime to undergo contraction, remain steady, or expand.