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 Lambda. The results are divided as follows. For small Lambda > 0 we show the existence of globally regular solutions which coincide with the Schwarzschild-deSitter solution in the exterior of the matter regions. For Lambda < 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 Lambda. 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 x S-3 and R x S-2 x 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.