Equilibrium configurations of fluids and their stability in higher dimensions

TL;DR

This paper explores the equilibrium shapes and stability of fluids in higher dimensions, revealing universal behaviors and analogies with general relativity phenomena like black rings and the Gregory-Laflamme instability.

Contribution

It generalizes the MacLaurin sequence to higher dimensions and establishes formalism linking fluid stability with relativistic black hole solutions.

Findings

Identifies an instability in self-gravitating fluid cylinders analogous to Gregory-Laflamme instability.

Recovers features of black rings using Newtonian fluid models.

Suggests universal dynamics in fluid stability across different models.

Abstract

We study equilibrium shapes, stability and possible bifurcation diagrams of fluids in higher dimensions, held together by either surface tension or self-gravity. We consider the equilibrium shape and stability problem of self-gravitating spheroids, establishing the formalism to generalize the MacLaurin sequence to higher dimensions. We show that such simple models, of interest on their own, also provide accurate descriptions of their general relativistic relatives with event horizons. The examples worked out here hint at some model-independent dynamics, and thus at some universality: smooth objects seem always to be well described by both ``replicas'' (either self-gravity or surface tension). As an example, we exhibit an instability afflicting self-gravitating (Newtonian) fluid cylinders. This instability is the exact analogue, within Newtonian gravity, of the Gregory-Laflamme instability in general relativity. Another example considered is a self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We recover the features of the black ring in general relativity.