Weakly regular T2 symmetric spacetimes. The global geometry of future developments

Details Weakly regular T2 symmetric spacetimes. The global geometry of future developments Weakly regular T2 symmetric spacetimes. The global geometry of future developments

2010-12-29

arxiv.org/abs/1012.5931v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

50 pages

Scientific paper

Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate the global causal structure of the constructed spacetimes. Our weak regularity assumptions are the minimal ones allowing to give a meaning to the Einstein equations under the assumed symmetry and to solve the initial value problem. First of all, we introduce a frame adapted to the symmetry in which each Christoffel symbol can be checked to belong to some Lp space. We identify certain cancellation properties taking place in the expression of the Riemann and Ricci curvatures, and this leads us to a reformulation of the initial value problem for the Einstein field equations when the initial data set has weak regularity. Second, we investigate the future development of a weakly regular initial data set. We check that the area R of the orbits of symmetry must grow to infinity in the future timelike directions, and we establish the existence of a global foliation by the level sets of R. Our weak regularity assumptions only require that R is Lipschitz continuous while the metric coefficients describing the initial geometry of the orbits of symmetry are in the Sobolev space H1 and the remaining coefficients have even weaker regularity. We develop here the compactness arguments required to cover the natural level of regularity associated with the energy of the system of partial differential equations determined from Einstein's field equations.

Affiliated with

Also associated with

No associations

Rating

Weakly regular T2 symmetric spacetimes. The global geometry of future developments does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weakly regular T2 symmetric spacetimes. The global geometry of future developments, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weakly regular T2 symmetric spacetimes. The global geometry of future developments will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-610859