Exact non-static cylindrical solutions of Einstein’s field equations with imperfect fluids

This work systematically derives a broad class of exact cylindrically symmetric spacetime models possessing scaling symmetries of varying dimensions. These models are then used to solve Einstein’s field equations for an imperfect fluid source that yields explicit anisotropic energy-momentum distributions. The solutions include vacuum, anisotropic fluid, and wave-like geometries, with connections to known models such as cylindrical waves, Levi-Civita spacetimes, and Kasner-type expansions. This study extends the catalog of exact cylindrically symmetric solutions and illustrates how scaling symmetry organizes the physics of time-dependent, anisotropic spacetimes.