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

Abstract In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying $p=\gamma \rho$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mip</mml:mi> mml:mo=</mml:mo> mml:miγ</mml:mi> mml:miρ</mml:mi> </mml:mrow> </mml:math> ( $0\le \gamma \le 1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mn0</mml:mn> mml:mo≤</mml:mo> mml:miγ</mml:mi> mml:mo≤</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:math> ), where $\gamma =1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miγ</mml:mi> mml:mo=</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:math> 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 $\delta = 1, 0, -1,$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miδ</mml:mi> mml:mo=</mml:mo> mml:mn1</mml:mn> mml:mo,</mml:mo> mml:mn0</mml:mn> mml:mo,</mml:mo> mml:mo-</mml:mo> mml:mn1</mml:mn> mml:mo,</mml:mo> </mml:mrow> </mml:math> 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.