24,716 research outputs found
Equilibrium configurations of fluids and their stability in higher dimensions
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.Comment: 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical
and Quantum Gravity. v2: Minor corrections and references adde
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)
An effective-gravity perspective on the Sun-Jupiter-comet three-body system
Within the solar system, approximate realizations of the three-body problem
occur when a comet approaches a planet while being affected mainly by such a
planet and the Sun, and this configuration was investigated by Tisserand within
the framework of Newtonian gravity. The exact relativistic treatment of the
problem is not an easy task, but the present paper develops an approximate
calculational scheme which computes for the first time the tiny
effective-gravity correction to the equation of the surface for all points of
which it is equally advantageous to regard the heliocentric motion as being
perturbed by the attraction of Jupiter, or the jovicentric motion as being
perturbed by the attraction of the Sun. This analysis completes the previous
theoretical investigations of effective-gravity corrections to the Newtonian
analysis of three-body systems, and represents an intermediate step towards
relativistic effects on cometary motions.Comment: Published versio
- …