Equilibrium configurations of fluids and their stability in higher dimensions

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.

arXiv comment42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical and Quantum Gravity. v2: Minor corrections and references added

References in corpus (35)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• The World as a Hologram
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• Black Strings and p-Branes are Unstable
• A rotating black ring in five dimensions
• A Covariant Entropy Conjecture
• Holography and hydrodynamics: diffusion on stretched horizons
• Classical Black Hole Production in High-Energy Collisions
• Phenomenology of Forward Hadrons in DIS: Fracture Functions and its $Q^2$ Evolution
• The Instability of Charged Black Strings and p-Branes
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Instability of Ultra-Spinning Black Holes
• On non-uniform black branes
• An Action for Black Hole Membranes
• Gravitational Radiation in D-dimensional Spacetimes
• A critical dimension in the black-string phase transition
• Quasinormal modes of Schwarzschild black holes in four and higher dimensions
• Black Rings, Supertubes, and a Stringy Resolution of Black Hole Non-Uniqueness
• Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity
• Gravitational energy loss in high energy particle collisions: ultrarelativistic plunge into a multidimensional black hole
• Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings
• Black Rings, Boosted Strings and Gregory-Laflamme
• Charged Rotating Black Holes in Odd Dimensions
• On Black-Brane Instability In an Arbitrary Dimension
• Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids
• Scalar-gravitational perturbations and quasinormal modes in the five dimensional Schwarzschild black hole
• Relativistic Dyson Rings and Their Black Hole Limit
• Black hole formation through fragmentation of toroidal polytropes
• Surface tension, hydrophobicity, and black holes: The entropic connection
• The Final State of Black Strings and p-Branes, and the Gregory-Laflamme Instability
• Ellipsoidal configurations in the de Sitter spacetime

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• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
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• Bar-mode instability of rapidly spinning black hole in higher dimensions: Numerical simulation in general relativity
• Polygonal excitations of spinning and levitating droplets
• Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes
• Black Holes as Lumps of Fluid
• Exploring New Physics Frontiers Through Numerical Relativity
• Instability of hyper-compact Kerr-like objects
• Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests
• Dyonic AdS black holes from magnetohydrodynamics
• Black Holes in Higher-Dimensional Gravity
• Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales
• Plasmarings as dual black rings
• Bubble Dynamics in N Dimensions
• Multi-black hole configurations on the cylinder
• Bifurcation of Plasma Balls and Black Holes to Lobed Configurations
• Black hole-black string phase transitions from hydrodynamics
• Thermodynamics of Plasmaballs and Plasmarings in 3+1 Dimensions
• Rotating nonuniform black string solutions
• The return of the membrane paradigm? Black holes and strings in the water tap
• Liquid bridges and black strings in higher dimensions
• Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme
• Phase diagram for non-axisymmetric plasma balls
• Velocity and velocity bounds in static spherically symmetric metrics
• One-Dimensional Approximation of Viscous Flows
• Gregory-Laflamme instability of a slowly rotating black string
• Instability of Compressible Drops and Jets
• A criterion on instability of rotating cylindrical surfaces