Rotating Cylinders with Anisotropic Fluids in General Relativity

Abstract

We consider anisotropic fluids with directional pressures p i = w i ρ (ρ is the density, w i = const, i = 1, 2, 3 ) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining exact solutions with such sources, where the main features are splitting of the Ricci tensor into static and rotational parts and using the harmonic radial coordinate. Depending on the values of w i , it appears possible to obtain general or special solutions to the Einstein equations, thus recovering some known solutions and finding new ones. Three particular examples of exact solutions are briefly described: with a stiff isotropic perfect fluid (p = ρ), with a distribution of cosmic strings of azimuthal direction (i.e., forming circles around the z axis), and with a stationary combination of two opposite radiation flows along the z axis.

Rotating Melvin-like Universes and Wormholes in General Relativity

“…In a perfect fluid with the equation of state p = ρ, the speed of sound is equal to the speed of light, which greatly simplifies the equations of motion and has led to obtaining numerous solutions which are either unique or much simpler than their counterparts with other equations of state: see, e.g., [27,33] for a general exposition, [34][35][36][37] for static solutions, [38] for wavy ones, and [39][40][41][42][43] for stationary ones; applications of stiff matter in modern theoretical cosmology can also be mentioned, see, e.g., [44,45]; see also references therein.…”

Hybrid Metric-Palatini Gravity: Regular Stringlike Configurations

“…In (48), we have used the fact that η = (dη/dψ)ψ vanishes as x → ∞, since ψ → 0 (see (44)), while dη/dψ must be finite due to the the regularity requirement for η(ψ).…”

“…Here we have discussed only static cylindrically symmetric configurations, but probably of even greater interest can be stringlike models with rotation, for which numerous solutions are known in GR (see, e.g., [23,24,44]), and their extensions to HMPG are quite possible.…”

Structure scalars and their evolution for massive objects in f(R) gravity

“…They concluded that their work is specifically useful in blackhole paradigm. Bolokhov et al [14] considered stationary cylindrically symmetric spacetimes along with anisotropic fluid distributions having directional pressures as the expected source of gravity. Keeping in view such sources, they investigated a way to obtain exact solutions by the splitting of Ricci tensor into rotational and static parts.…”