Cylindrically Symmetric Scalar Field and its Lyapunov stability in General Relativity
arXiv:1009.0168 · doi:10.1007/s10773-010-0509-9
Abstract
In this paper we found an Exact solution for massless scalar field with cosmological constant. This exact solution generalized the Levi-Civita vacuum solution\cite{8} to a massless scalar field,with a cosmological constant term. This solution in the absence of the Cosmological constant recovers the spacetime of a massless scalar field with cylindrical symmetry (\emph{Buchdahl metric}\cite{2}). Also if the scalar field disappears, the spacetime is a representation of de-Sitter space. We prove that the form of the metric's function which was purposed in \cite{1} is valid even if we assume a general form. Too we show that in which conditions this solution satisfies energy conditions. Finally the validity of focusing theorem is proved.
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