The effective geometry of the $n=1$ uniformly rotating self-gravitating polytrope

TL;DR

This paper explores the geometric properties of perturbations in a rotating, self-gravitating fluid modeled as a polytrope with index n=1, using an effective geometry approach to analyze acoustic metrics and null geodesics.

Contribution

It introduces an analytical study of the effective acoustic geometry of a rotating polytrope with n=1, highlighting its null geodesics and light cone structure.

Findings

Analysis of null geodesics in the acoustic metric

Characterization of the effective light cone structure

Insights into the geometrical properties of rotating fluid perturbations

Abstract

The \lq\lq effective geometry" formalism is used to study the perturbations of a perfect barotropic Newtonian self-gravitating rotating and compressible fluid coupled with gravitational backreaction. The case of a uniformly rotating polytrope with index $n=1$ is investigated, due to its analytical tractability. Special attention is devoted to the geometrical properties of the underlying background acoustic metric, focusing in particular on null geodesics as well as on the analog light cone structure.