Static solutions to the Einstein-Vlasov system with a nonvanishing cosmological constant
Journal article, 2015

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.

Static solutions

Black holes

Schwarzschild-deSitter

Schwarzschild-anti-deSitter

Einstein equations

Einstein-Vlasov system

Author

Håkan Andreasson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

D. Fajman

University of Vienna

Maximilian Thaller

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

SIAM Journal on Mathematical Analysis

0036-1410 (ISSN) 1095-7154 (eISSN)

Vol. 47 4 2657-2688

Subject Categories

Mathematics

Fusion, Plasma and Space Physics

DOI

10.1137/140999608

More information

Latest update

3/29/2018