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

TL;DR

This paper derives exact solutions for cylindrically symmetric spacetimes filled with a stiff fluid, exploring different metric behaviors and their implications for anisotropic cosmologies.

Contribution

It provides explicit, general solutions for cylindrically symmetric Einstein equations with a stiff fluid, covering exponential, power-law, and trigonometric metric functions.

Findings

Solutions exhibit anisotropic evolution with nontrivial expansion and shear.

Space-times have curvature singularities and specific energy density profiles.

Framework applicable to early-universe models and higher-dimensional theories.

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.