The Linet-Tian metrics are a restricted set of Krasi\'nski's solutions of Einstein's field equations for a rotating perfect fluid

TL;DR

This paper demonstrates that the Linet-Tian vacuum solutions with a cosmological constant are a special case of Krasiński's rotating perfect fluid solutions in Einstein's field equations.

Contribution

It establishes a direct link between the Linet-Tian solutions and Krasiński's solutions, clarifying their relationship within Einstein's equations.

Findings

Linet-Tian solutions are a subset of Krasiński's solutions.

The solutions describe rotating perfect fluids with specific restrictions.

The work unifies two previously separate classes of solutions.

Abstract

In this note we show that the Linet-Tian family of solutions of the vacuum Einstein equations with a cosmological constant are a restricted set of the solutions of the Einstein field equations for a rotating perfect fluid previously found by A. Krasi\'nski.