Stationary Cylindrical Anisotropic Fluid

Abstract

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful stationary cylindrically symmmetric distributions of matter, smoothly matched to Lewis vacuum spacetime. A specific example is given. The electric and magnetic parts of the Weyl tensor are calculated, and it is shown that purely electric solutions are necessarily static. Then, it is shown that no conformally flat stationary cylindrical fluid exits, satisfying regularity and matching conditions.

17 pages Latex. To appear in Gen.Rel.Grav

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• Stationary cylindrical anisotropic fluid and new purely magnetic GR solutions
• New classes of exact interior nonvacuum solutions to the GR field equations for spacetimes sourced by a rigidly rotating stationary cylindrical anisotropic fluid
• Generating anisotropic fluids from vacuum Ernst equations
• Some unusual wormholes in general relativity
• On the Relativistic anisotropic configurations
• Rotating cylinders with anisotropic fluids in general relativity
• Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. 5. Dust limit and discussion
• Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. 4. Radial pressure
• Matching stationary spacetimes
• Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids
• String clouds and radiation flows as sources of gravity in static or rotating cylinders
• Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids: anisotropic pressure
• Non-rigidly rotating stationary cylindrical dust spacetimes