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

Journal article
Authors Håkan Andreasson
D. Fajman
Maximilian Thaller
Published in SIAM Journal on Mathematical Analysis
Volume 47
Issue 4
Pages 2657-2688
ISSN 0036-1410
Publication year 2015
Published at Department of Mathematical Sciences, Mathematics
Pages 2657-2688
Language en
Links dx.doi.org/10.1137/140999608
https://gup.ub.gu.se/file/205166
Keywords Black holes , Einstein equations , Einstein-Vlasov system , Schwarzschild-anti-deSitter , Schwarzschild-deSitter , Static solutions
Subject categories Mathematics, Space physics

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.

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