Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
Journal article, 2010
We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.
static solutions
poisson system
matter
newtonian
field
trapped surfaces
singularities
weak cosmic censorship
limit
Einstein-Vlasov system
gravitational collapse
regularity
cosmic censorship
black-holes
Author
Håkan Andreasson
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
G. Rein
University of Bayreuth
Journal of Hyperbolic Differential Equations
0219-8916 (ISSN)
Vol. 7 4 707-731Subject Categories
Computational Mathematics
Astronomy, Astrophysics and Cosmology
Mathematical Analysis
DOI
10.1142/S0219891610002268