2004
DOI: 10.1142/s0219891604000305
|View full text |Cite
|
Sign up to set email alerts
|

Local Existence and Continuation Criteria for Solutions of the Einstein–vlasov-Scalar Field System With Surface Symmetry

Abstract: We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological 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. This system describes the evolution of self-gravitating collisionless matter and scalar waves within the context of general relativity. In the case where the only source is a scalar field i… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

4
30
0

Year Published

2005
2005
2013
2013

Publication Types

Select...
7
2

Relationship

1
8

Authors

Journals

citations
Cited by 63 publications
(34 citation statements)
references
References 24 publications
4
30
0
Order By: Relevance
“…(A similar structure was observed in [11].) A specific technical difficulty overcome in this work originates in the fact that solutions may naturally contain vacuum states as well as velocities approaching the speed of light, both possibilities leading to singular behavior in the evolution equations.…”
Section: Introductionsupporting
confidence: 57%
“…(A similar structure was observed in [11].) A specific technical difficulty overcome in this work originates in the fact that solutions may naturally contain vacuum states as well as velocities approaching the speed of light, both possibilities leading to singular behavior in the evolution equations.…”
Section: Introductionsupporting
confidence: 57%
“…It would be interesting to see to what extent these results can be generalized to nonlinear scalar fields with potentials which give accelerated expansion in the homogeneous case. The results of [31] on the Einstein-Vlasov system coupled to a linear scalar field are a first step in this direction. Note that the use of collisionless matter in these results is not an accident.…”
Section: Resultsmentioning
confidence: 99%
“…In the case of Collisionless matter, the phenomena are governed by the Einstein-Vlasov system in the pure gravitational case, and by this system coupled to other fields equations, if other fields than the gravitational field are involved. In the collisionless case, several authors proved global results, see [1], [19] for reviews, [18], [23] and [3] for scalar matter fields, also see [21], [22] for the Einstein-Vlasov system with a cosmological constant. Now in the case of Collisional matter, the Einstein-Vlasov system is replaced by the Einstein-Boltzmann system, that seems to be the best approximation available and that describes the case of instantaneous, binary and elastic collisions.…”
Section: Introductionmentioning
confidence: 99%