Static cylindrically symmetric spacetimes
Mikael Fjallborg
TL;DR
This paper proves the existence of static cylindrically symmetric solutions in Einstein-Vlasov and related systems, showing matter cylinders have finite size and extending results to general equations of state and Vlasov-Poisson.
Contribution
It establishes the existence of finite, static, cylindrically symmetric solutions for Einstein-Vlasov, perfect fluids, and Vlasov-Poisson systems, broadening previous classes of equations considered.
Findings
Existence of static solutions with finite matter cylinders
Extension to general equations of state for perfect fluids
Applicability to Vlasov-Poisson system
Abstract
We prove existence of static solutions to the cylindrically symmetric Einstein-Vlasov system, and we show that the matter cylinder has finite extension. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered in \cite{BL}. We also obtain this result for the Vlasov-Poisson system.
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