Axistationary perfect fluids -- a tetrad approach

TL;DR

This paper studies stationary axisymmetric perfect fluid spacetimes using a tetrad approach, revealing that the only incompressible magnetic perfect fluid solution is Schwarzschild's interior, and proving the existence of a generalized rigidly rotating fluid solution.

Contribution

It introduces a tetrad-based analysis of axisymmetric perfect fluids, identifying unique solutions and establishing new theorems on spacetime properties.

Findings

Only the interior Schwarzschild solution is an incompressible magnetic perfect fluid.

A generalized rigidly rotating perfect fluid solution exists.

Theorems on Petrov types and Weyl tensor properties are established.

Abstract

Stationary axisymmetric perfect fluid space-times are investigated using the curvature description of geometries. Attention is focused on space-times with a vanishing electric part of the Weyl tensor. It is shown that the only incompressible axistationary magnetic perfect fluid is the interior Schwarzschild solution. The existence of a rigidly rotating perfect fluid, generalizing the interior Schwarzschild metric is proven. Theorems are stated on Petrov types and electric/magnetic Weyl tensors.