Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids

TL;DR

This paper presents a fully integrated class of interior solutions for stationary rotating cylindrical perfect fluids in General Relativity, deriving the equation of state directly from Einstein's field equations using a novel ansatz.

Contribution

It introduces a new ansatz that enables obtaining exact interior solutions with a natural equation of state from Einstein's equations.

Findings

Derived a class of exact solutions using simple analytical functions.

Demonstrated the equation of state emerges naturally from the solutions.

Extended previous work by Krasiński with a new integrative approach.

Abstract

In an important series of articles published during the 70's, Krasi\'nski displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotating cylinder of perfect fluid. However, these solutions depend on an unspecified arbitrary function, which lead the author to claim that the equation of state of the fluid could not be obtained directly from the field equations but had to be added by hand. In the present article, we use a double ansatz which we have developed in 2021 and implemented at length into a series of recent papers displaying exact interior solutions for a stationary rotating cylindrically symmetric fluid with anisotropic pressure. This ansatz allows us to obtain here a fully integrated class of solutions to the Einstein equations, written with the use of very simple analytical functions, and to show that the equation of state of the fluid follows naturally from these field equations.