Static solutions to the Einstein-Vlasov system with a nonvanishing cosmological constant
Artikel i vetenskaplig tidskrift, 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

Författare

Håkan Andreasson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

D. Fajman

Universität Wien

Maximilian Thaller

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

SIAM Journal on Mathematical Analysis

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

Vol. 47 2657-2688

Ämneskategorier

Matematik

Fusion, plasma och rymdfysik

DOI

10.1137/140999608