scholarly journals A non-existence result for a generalization of the equations of the conformal method in general relativity

2013 ◽  
Vol 30 (7) ◽  
pp. 075004
Author(s):  
Mattias Dahl ◽  
Romain Gicquaud ◽  
Emmanuel Humbert
Keyword(s):  
General Relativity ◽  
Existence Result ◽  
Conformal Method

scholarly journals LOCAL EXISTENCE AND CONTINUATION CRITERIA FOR SOLUTIONS OF THE EINSTEIN–VLASOV-SCALAR FIELD SYSTEM WITH SURFACE SYMMETRY

2004 ◽  
Vol 01 (04) ◽  
pp. 691-724 ◽  
Author(s):  
D. TEGANKONG ◽  
N. NOUTCHEGUEME ◽  
A. D. RENDALL
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Wave Equations ◽  
Existence Result ◽  
General Theorem ◽  
Local Existence ◽  
Field System ◽  
Cosmological Solutions ◽  
Time Existence ◽  
Global Existence Result

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 it is shown that a global existence result can be deduced from the general theorem.

scholarly journals Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry

1996 ◽  
Vol 119 (4) ◽  
pp. 739-762 ◽  
Author(s):  
Gerhard Rein
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Existence Result ◽  
Local Existence ◽  
Space Distribution ◽  
Initial Value ◽  
Small Initial Data ◽  
Phase Space Distribution ◽  
Spacetime Singularity ◽  
Cosmological Solutions

AbstractThe Vlasov-Einstein system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with spherical, plane, or hyperbolic symmetry and prove that for small initial data solutions exist up to a spacetime singularity which is a curvature and a crushing singularity. An important tool in the analysis is a local existence result with a continuation criterion saying that solutions can be extended as long as the momenta in the support of the phase-space distribution of the matter remain bounded.

General Relativity

2006 ◽  
Author(s):  
M. P. Hobson ◽  
G. P. Efstathiou ◽  
A. N. Lasenby
Keyword(s):  
General Relativity

Generation of cosmological flows in General Relativity

2012 ◽  
Vol 182 (8) ◽  
pp. 894 ◽  
Author(s):  
Vladimir N. Lukash ◽  
Elena V. Mikheeva ◽  
Vladimir N. Strokov
Keyword(s):  
General Relativity
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