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arXiv · 1009.0168

Cylindrically Symmetric Scalar Field and its Lyapunov stability in General Relativity

H. R. Rezazadeh
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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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H. R. Rezazadeh. 2010-09-01. Cylindrically Symmetric Scalar Field and its Lyapunov stability in General Relativity. https://doi.org/10.1007/s10773-010-0509-9

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