Static, Cylindrically Symmetric Perfect Fluid Configurations

We study the properties of static, cylindrically symmetric configurations of a perfect fluid in general relativity, with the equation of state p = ωε with arbitrary values ω = const. We thus include into consideration the types of fluids which are now actively studied in cosmology (dark matter, cosmic strings, domain walls, quintessence, cosmic vacuum, phantom matter). Exact solutions to the Einstein equations with such fluids have been obtained for arbitrary values of ω. For any ω, we prove the absence of a flat spatial asymptotic as well as an asymptotic like that of a cosmic string. We show that all such distributions, under some conditions on the integration constants, have a regular axis and a spatial infinity at which the energy density tends to zero (except for configurations with ω = −1/3, which corresponds to a gas of cosmic strings). Thus such a system has a finite energy per unit length along the symmetry axis. In particular, for stiff matter (ω = 1), this quantity is equal to the Planck value of energy per unit length.

идеальная жидкость, уравнения Эйнштейна, уравнение состояния