52 research outputs found
Stability of relativistic Bondi accretion in Schwarzschild-(anti-)de Sitter spacetimes
In a recent paper we investigated stationary, relativistic Bondi-type
accretion in Schwarzschild-(anti-)de Sitter spacetimes. Here we study their
stability, using the method developed by Moncrief. The analysis applies to
perturbations satisfying the potential flow condition. We prove that global
isothermal flows in Schwarzschild-anti-de Sitter spacetimes are stable,
assuming the test-fluid approximation. Isothermal flows in Schwarzschild-de
Sitter geometries and polytropic flows in Schwarzschild-de Sitter and
Schwarzschild-anti-de Sitter spacetimes can be stable, under suitable boundary
conditions.Comment: 6 page
Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaitre-Robertson-Walker spacetimes: Stability and isoperimetric inequalities
We investigate toroidal Marginally Outer Trapped Surfaces (MOTS) and
Marginally Outer Trapped Tubes (MOTT) in closed
Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. They are constructed by
embedding Constant Mean Curvature (CMC) Clifford tori in a FLRW spacetime. This
construction is used to assess the quality of certain isoperimetric
inequalities, recently proved in axial symmetry. Similarly to spherically
symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also
unstable.Comment: 7 pages, 2 figure
Spherically symmetric Riemannian manifolds of constant scalar curvature and their conformally flat representations
All spherically symmetric Riemannian metrics of constant scalar curvature in
any dimension can be written down in a simple form using areal coordinates. All
spherical metrics are conformally flat, so we search for the conformally flat
representations of these geometries. We find all solutions for the conformal
factor in 3, 4 and 6 dimensions. We write them in closed form, either in terms
of elliptic or elementary functions. We are particularly interested in
3-dimensional spaces because of the link to General Relativity. In particular,
all 3-dimensional constant negative scalar curvature spherical manifolds can be
embedded as constant mean curvature surfaces in appropriate Schwarzschild
solutions. Our approach, although not the simplest one, is linked to the
Lichnerowicz-York method of finding initial data for Einstein equations.Comment: 18 pages, 3 figures, to appear in Class. Quantum Gra
Construction of vacuum initial data by the conformally covariant split system
Using the implicit function theorem, we prove existence of solutions of the
so-called conformally covariant split system on compact 3-dimensional
Riemannian manifolds. They give rise to non-Constant Mean Curvature (non-CMC)
vacuum initial data for the Einstein equations. We investigate the conformally
covariant split system defined on compact manifolds with or without boundaries.
In the former case, the boundary corresponds to an apparent horizon in the
constructed initial data. The case with a cosmological constant is then
considered separately. Finally, to demonstrate the applicability of the
conformal covariant split system in numerical studies, we provide numerical
examples of solutions on manifolds and
- …