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arXiv · 2604.02449

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

Tiberiu Harko·Francisco S. N. Lobo·Man Kwong Mak
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Abstract

In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying $p=\gamma \rho$ ($0\leq \gamma \leq 1$), where $\gamma=1$ 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 $\delta = 1, 0, -1$, 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.

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Tiberiu Harko, Francisco S. N. Lobo, Man Kwong Mak. 2026-04-02. Exact general relativistic solutions for a cylindrically symmetric stiff fluid matter source. https://doi.org/10.1140/epjc%2Fs10052-026-16225-7

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