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

• 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.

Ämnesord

NATURVETENSKAP  -- Fysik -- Fusion, plasma och rymdfysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Fusion, Plasma and Space Physics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Black holes

Einstein equations

Einstein-Vlasov system

Schwarzschild-anti-deSitter

Schwarzschild-deSitter

Static solutions

Static solutions

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ref (ämneskategori)

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