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://ucrisportal.univie.ac.at/en/publications/static-solutions-to-the-einsteinvlasov-system-with-a-nonvanishing-cosmological-constant(4f5b9ead-7b9e-40e9-a7e7-5b0ed6da307f).html