Equilibrium configurations of fluids and their stability in higher dimensions

Details Equilibrium configurations of fluids and their stability in higher dimensions Equilibrium configurations of fluids and their stability in higher dimensions

2006-09-29

arxiv.org/abs/hep-th/0610004v2

Class.Quant.Grav.23:7151-7198,2006

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical and Quantum Gravity. v2: Minor corrections and references

Scientific paper

10.1088/0264-9381/23/24/001

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.

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