Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. 2. More about axial pressure

TL;DR

This paper develops a general method for constructing exact interior solutions of stationary, rigidly rotating, anisotropic cylindrical fluids in General Relativity, focusing on axial pressure cases and their physical properties.

Contribution

It introduces a new comprehensive method for generating classes of exact solutions, including two novel solution classes, advancing understanding of rotating anisotropic cylinders in GR.

Findings

Validated solutions satisfy all physical and mathematical conditions.

Class A solutions meet regularity, matching, and energy conditions.

The method provides insights into longstanding issues in cylindrical GR solutions.

Abstract

This article is the second in a series devoted to the study of spacetimes sourced by a stationary cylinder of fluid rigidly rotating around its symmetry axis and exhibiting an anisotropic pressure by using new exact interior solutions of General Relativity. The configurations have been specialized to three different cases where the pressure is on turn directed alongside each principal stress. The two first articles in the series display the analysis of the axial pressure case. Indeed, the first axial class published in Paper 1 is merely a special case. It is recalled here and its properties are revised and supplemented. Moreover, a fully general method aiming at constructing different classes of such solutions is displayed. This method described in the present paper, Paper 2, represents a key result of this work. It is exemplified and applied to two new classes of solutions depending on a single constant parameter. One of them, denoted Class A, is shown to verify every conditions needing to be satisfied by a fully achieved set of exact solutions: axisymmetry and regularity conditions, matching to an exterior vacuum, proper metric signature, weak and strong energy conditions. Other properties and general rules are exhibited, some shedding light on rather longstanding issues. Astrophysical and physical applications are suggested.