Exact general relativistic solutions for a cylindrically symmetric stiff fluid matter source

In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying p=γ ρ p = γ ρ ( 0≤ γ ≤ 1 0 ≤ γ ≤ 1 ), where γ =1 γ = 1 represents a stiff or Zeldovich fluid. Using Marder’s metric with coefficients depending on t and r , we obtain explicit solutions of the gravitational field equations for the three cases δ = 1, 0, -1, δ = 1 , 0 , - 1 , corresponding to exponential, power-law, and trigonometric behaviors of the metric functions. The resulting space-times exhibit anisotropic evolution, nontrivial expansion and shear, and curvature singularities, with energy density and pressure profiles determined by the integration constants. These solutions provide a comprehensive framework for modeling cylindrically symmetric cosmologies, offering insights into early-universe dynamics and anisotropic gravitational phenomena. The versatility of the solutions also opens avenues for extensions to higher-dimensional or modified gravity scenarios, making them a valuable tool for both theoretical and phenomenological studies in general relativity.