Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. 5. Dust limit and discussion

TL;DR

This paper concludes a series on anisotropic rotating cylindrical fluids in General Relativity, presenting new exact solutions, revisiting fundamental concepts, and deriving a dust solution linked to the Lanczos-van Stockum spacetime.

Contribution

It provides a comprehensive synthesis of previous results, introduces a new derivation of the dust solution, and clarifies its relation to a classical spacetime in GR.

Findings

New exact interior solutions for rotating anisotropic cylinders

Revisiting causality, regularity, and energy conditions in these solutions

Derivation of a dust solution corresponding to the Lanczos-van Stockum spacetime

Abstract

The present article is the last in a series of five devoted to the study of the effect of anisotropic pressure on the gravitationnal impact of a stationary rigidly rotating cylindrically symmetric fluid with the use of new exact solutions of General Relativity. In the four first papers in this series, three kinds of pressures directed each along one of the principal stresses of the fluid have been considered and new interior solutions of the field equations have been constructed and analyzed. Here, key results and issues raised in these previous works are synthesized and some fundamental notions of general relativity, causality, regularity of Lorentzian manifolds, elementary flatness in the vicinity of a symmetry axis, singularities, physics of angular deficits, weak and strong energy conditions, are revisited. Then, a new derivation of the corresponding dust solution is displayed and shown to correspond indeed to the Lanczos-van Stockum solution shedding new light to this well-known spacetime.