54 research outputs found
A Conformal Extension Theorem based on Null Conformal Geodesics
In this article we describe the formulation of null geodesics as null
conformal geodesics and their description in the tractor formalism. A conformal
extension theorem through an isotropic singularity is proven by requiring the
boundedness of the tractor curvature and its derivatives to sufficient order
along a congruence of null conformal geodesic. This article extends earlier
work by Tod and Luebbe.Comment: 20 pages, no figures, version as published in JMP, updated reference
A global conformal extension theorem for perfect fluid Bianchi space-times
A global extension theorem is established for isotropic singularities in
polytropic perfect fluid Bianchi space-times. When an extension is possible,
the limiting behaviour of the physical space-time near the singularity is
analysed.Comment: 13 pages, no figures, revised and shortened, improved proof of main
theorem, some correction
A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies
The conformal Einstein equations for a tracefree (radiation) perfect fluid
are derived in terms of the Levi-Civita connection of a conformally rescaled
metric. These equations are used to provide a non-linear stability result for
de Sitter-like tracefree (radiation) perfect fluid
Friedman-Lema\^{\i}tre-Robertson-Walker cosmological models. The solutions thus
obtained exist globally towards the future and are future geodesically
complete.Comment: 21 page
An extension theorem for conformal gauge singularities
We analyse conformal gauge, or isotropic, singularities in cosmological
models in general relativity. Using the calculus of tractors, we find
conditions in terms of tractor curvature for a local extension of the conformal
structure through a cosmological singularity and prove a local extension
theorem.Comment: 43 pages, no figures, version as published in JMP, small changes,
updated reference
The extended Conformal Einstein field equations with matter: the Einstein-Maxwell field
A discussion is given of the conformal Einstein field equations coupled with
matter whose energy-momentum tensor is trace-free. These resulting equations
are expressed in terms of a generic Weyl connection. The article shows how in
the presence of matter it is possible to construct a conformal gauge which
allows to know \emph{a priori} the location of the conformal boundary. In
vacuum this gauge reduces to the so-called conformal Gaussian gauge. These
ideas are applied to obtain: (i) a new proof of the stability of
Einstein-Maxwell de Sitter-like spacetimes; (ii) a proof of the semi-global
stability of purely radiative Einstein-Maxwell spacetimes.Comment: 29 page
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