2006/10/13 by Vitor Cardoso, Vítor Cardoso, Leonardo Gualtieri · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #astro-ph #gr-qc #hep-ph #hep-th #physics.flu-dyn
paper · pdf · doi:10.1088/0264-9381/23/24/001
published as Class.Quant.Grav.23:7151-7198,2006 · 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical and Quantum Gravity. v2: Minor corrections and references added
arxiv created 2006/10/13 · openalex publication_date 2006/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.