652 research outputs found
Coupled quintessence and curvature-assisted acceleration
Spatially homogeneous models with a scalar field non-minimally coupled to the
space-time curvature or to the ordinary matter content are analysed with
respect to late-time asymptotic behaviour, in particular to accelerated
expansion and isotropization. It is found that a direct coupling to the
curvature leads to asymptotic de Sitter expansion in arbitrary exponential
potentials, thus yielding a positive cosmological constant although none is
apparent in the potential. This holds true regardless of the steepness of the
potential or the smallness of the coupling constant. For matter-coupled scalar
fields, the asymptotics are obtained for a large class of positive potentials,
generalizing the well-known cosmic no-hair theorems for minimal coupling. In
this case it is observed that the direct coupling to matter does not impact the
late-time dynamics essentially.Comment: 17 pages, no figures. v2: typos correcte
Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
We prove in the cases of plane and hyperbolic symmetries a global in time
existence result in the future for comological solutions of the
Einstein-Vlasov-scalar field system, with the sources generated by a
distribution function and a scalar field, subject to the Vlasov and wave
equations respectively. The spacetime is future geodesically complete in the
special case of plane symmetry with only a scalar field. Causal geodesics are
also shown to be future complete for homogeneous solutions of the
Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.Comment: 14 page
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
Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry
The late-time behaviour of the Einstein-dust system is well understood for
homogeneous spacetimes. For the case of Bianchi I we have been able to show
that the late-time behaviour of the Einstein-Vlasov system is well approximated
by the Einstein-dust system assuming that one is close to the unique stationary
solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting
2010, to appear in Journal of Physics: Conference Series (JPCS
Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry
The late-time behaviour of the Einstein-dust system is well understood for
homogeneous spacetimes. For the case of Bianchi I we have been able to show
that the late-time behaviour of the Einstein-Vlasov system is well approximated
by the Einstein-dust system assuming that one is close to the unique stationary
solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting
2010, to appear in Journal of Physics: Conference Series (JPCS
Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry
The late-time behaviour of the Einstein-dust system is well understood for
homogeneous spacetimes. For the case of Bianchi I we have been able to show
that the late-time behaviour of the Einstein-Vlasov system is well approximated
by the Einstein-dust system assuming that one is close to the unique stationary
solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting
2010, to appear in Journal of Physics: Conference Series (JPCS
Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system
Using ODE techniques we prove the existence of large classes of initial data
satisfying the constraints for the spherically symmetric
Einstein-Vlasov-Maxwell system. These include data for which the ratio of total
charge to total mass is arbitrarily large.Comment: 12 page
Fuchsian methods and spacetime singularities
Fuchsian methods and their applications to the study of the structure of
spacetime singularities are surveyed. The existence question for spacetimes
with compact Cauchy horizons is discussed. After some basic facts concerning
Fuchsian equations have been recalled, various ways in which these equations
have been applied in general relativity are described. Possible future
applications are indicated
Late-time oscillatory behaviour for self-gravitating scalar fields
This paper investigates the late-time behaviour of certain cosmological
models where oscillations play an essential role. Rigorous results are proved
on the asymptotics of homogeneous and isotropic spacetimes with a linear
massive scalar field as source. Various generalizations are obtained for
nonlinear massive scalar fields, -essence models and gravity. The
effect of adding ordinary matter is discussed as is the case of nonlinear
scalar fields whose potential has a degenerate zero.Comment: 17 pages, additional reference
Local and global existence theorems for the Einstein equations
This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first. Next global results for solutions with symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. This is followed by a survey of global results in the case of small data and results on constructing spacetimes with given singularity structure. The article ends with some miscellaneous topics connected with the main theme
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