Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. IV. Radial pressure

TL;DR

This paper extends previous work on interior solutions of rotating cylindrical fluids in General Relativity to include radially pressured irrotational fluids, identifying four solution classes and analyzing their properties.

Contribution

It introduces new exact solutions for differentially rotating irrotational fluids with radial pressure, expanding the understanding of interior cylindrical spacetime models.

Findings

Classes I and III solutions are fully integrated and analyzed.

Class III is ruled out due to metric signature issues.

Simplified differential equations are provided for further numerical study.

Abstract

In a recent series of papers new exact analytical solutions of the field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been displayed. This work is currently extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering, in turn, a perfect fluid source, as well as the three anisotropic pressure cases already studied in the rigidly rotating configuration. Here, we analyze the case of a fluid with radially directed pressure. Four classes of solutions are identified from the field equations. Among them, class I and III are fully integrated, and their mathematical and physical properties are studied, which implies a ruling out of class III for lack of proper metric signature. For each of the two other classes, a set of simplified differential equation is displayed so as to ease their possible further numerical integration. Finally, a comparison with the corresponding rigidly rotating fluid solution is provided.