14 research outputs found
Inextendibility of expanding cosmological models with symmetry
A new criterion for inextendibility of expanding cosmological models with
symmetry is presented. It is applied to derive a number of new results and to
simplify the proofs of existing ones. In particular it shows that the solutions
of the Einstein-Vlasov system with symmetry, including the vacuum
solutions, are inextendible in the future. The technique introduced adds a
qualitatively new element to the available tool-kit for studying strong cosmic
censorship.Comment: 7 page
Strong cosmic censorship for solutions of the Einstein-Maxwell field equations with polarized Gowdy symmetry
A proof of strong cosmic censorship is presented for a class of solutions of
the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key
element of the argument is the observation that by means of a suitable choice
of variables the central equations in this problem can be written in a form
where they are identical to the central equations for general (i.e.
non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the deep
results of Ringstr\"om on strong cosmic censorship in the vacuum case have
implications for the Einstein-Maxwell case. Working out the geometrical meaning
of these analytical results leads to the main conclusion.Comment: Some references have been change
Odd-parity perturbations of self-similar Vaidya spacetime
We carry out an analytic study of odd-parity perturbations of the
self-similar Vaidya space-times that admit a naked singularity. It is found
that an initially finite perturbation remains finite at the Cauchy horizon.
This holds not only for the gauge invariant metric and matter perturbation, but
also for all the gauge invariant perturbed Weyl curvature scalars, including
the gravitational radiation scalars. In each case, `finiteness' refers to
Sobolev norms of scalar quantities on naturally occurring spacelike
hypersurfaces, as well as pointwise values of these quantities.Comment: 28 page
On the relation between mathematical and numerical relativity
The large scale binary black hole effort in numerical relativity has led to
an increasing distinction between numerical and mathematical relativity. This
note discusses this situation and gives some examples of succesful interactions
between numerical and mathematical methods is general relativity.Comment: 12 page
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)
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
This article reviews some aspects in the current relationship between
mathematical and numerical General Relativity. Focus is placed on the
description of isolated systems, with a particular emphasis on recent
developments in the study of black holes. Ideas concerning asymptotic flatness,
the initial value problem, the constraint equations, evolution formalisms,
geometric inequalities and quasi-local black hole horizons are discussed on the
light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity.
Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24
November, 2006), part of the "General Relativity Trimester" at the Institut
Henri Poincare (Fall 2006). Comments and references added. Typos corrected.
Submitted to Classical and Quantum Gravit