Static fluid cylinders and their fields: global solutions

TL;DR

This paper investigates the global properties of static perfect-fluid cylinders and their external fields, demonstrating existence, uniqueness, and finite radii conditions through analytical and numerical methods.

Contribution

It provides new analytical and numerical solutions for static fluid cylinders with various equations of state, including relativistic cases.

Findings

Existence and uniqueness of solutions for general equations of state.

Finite radius condition for fluids with non-zero density at zero pressure.

Analytical solutions for nearly Newtonian cylinders and numerical solutions for relativistic cases.

Abstract

The global properties of static perfect-fluid cylinders and their external Levi-Civita fields are studied both analytically and numerically. The existence and uniqueness of global solutions is demonstrated for a fairly general equation of state of the fluid. In the case of a fluid admitting a non-vanishing density for zero pressure, it is shown that the cylinder's radius has to be finite. For incompressible fluid, the field equations are solved analytically for nearly Newtonian cylinders and numerically in fully relativistic situations. Various physical quantities such as proper and circumferential radii, external conicity parameter and masses per unit proper/coordinate length are exhibited graphically.