Static solutions to the Einstein-Vlasov system with a nonvanishing cosmological constant

Author(s)
Hakan Andreasson, David Fajman, Maximilian Thaller
Abstract

We construct spherically symmetric static solutions to the Einstein-Vlasov system with nonvanishing cosmological constant Λ. The results are divided as follows. For small Λ > 0 we show the existence of globally regular solutions which coincide with the Schwarzschild-deSitter solution in the exterior of the matter regions. For Λ < 0 we show via an energy estimate the existence of globally regular solutions which coincide with the Schwarzschild-anti-deSitter solution in the exterior vacuum region. We also construct solutions with a Schwarzschild singularity at the center regardless of the sign of Λ. For all solutions considered, the energy density and the pressure components have bounded support. Finally, we point out a straightforward method for obtaining a large class of global, nonvacuum spacetimes with topologies ℝ × S3 and ℝ × S2 × ℝ which arise from our solutions as a result of using the periodicity of the Schwarzschild-deSitter solution. A subclass of these solutions contains black holes of different masses.

Organisation(s)
Gravitational Physics
External organisation(s)
University of Gothenburg, Chalmers University of Technology
Journal
SIAM Journal on Mathematical Analysis
Volume
47
Pages
2657-2688
No. of pages
32
ISSN
0036-1410
DOI
https://doi.org/10.1137/140999608
Publication date
2015
Peer reviewed
Yes
Austrian Fields of Science 2012
103036 Theoretical physics, 103019 Mathematical physics
Keywords
ASJC Scopus subject areas
Computational Mathematics, Analysis, Applied Mathematics
Portal url
https://ucris.univie.ac.at/portal/en/publications/static-solutions-to-the-einsteinvlasov-system-with-a-nonvanishing-cosmological-constant(4f5b9ead-7b9e-40e9-a7e7-5b0ed6da307f).html