Equilibrium Configurations of Homogeneous Fluids in General Relativity

TL;DR

This paper explores the solution space of rotating homogeneous fluids in general relativity, revealing new classes of solutions and their relation to Newtonian limits, using a highly accurate spectral method.

Contribution

It introduces two new classes of relativistic fluid solutions, including core-ring and two-ring configurations, expanding understanding of equilibrium states in relativistic fluids.

Findings

Identification of multiple solution classes in relativistic fluid configurations.

Relativistic solutions connect to Newtonian limits through infinite classes.

The relativistic disc of dust is reached after an infinite sequence of classes.

Abstract

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated, can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust.