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Journal of Physical Studies 20(1/2), Article 1002 [8 pages] (2016)
DOI: https://doi.org/10.30970/jps.20.1002 ON THE QUALITATIVE ANALYSIS OF SOME STATIC CYLINDRICALLY SYMMETRIC SOLUTIONS OF THE EINSTEIN EQUATIONSS. B. Grigoryev, A. B. Leonov
Oles Honchar Dnipropetrovsk National University |
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We perform a qualitative analysis of the cylindrically symmetric static Einstein equations with the diagonal stress-energy tensor with mutually proportional components. This case simultaneously covers several important exact solutions, such as the solution with the static electric field, the perfect fluid a solution, solution with the cosmological constant and the massless scalar field solution. The problem involves the analysis of the system in a neighborhood of a non-hyperbolic equilibrium point. However, due to the properties of the system it is possible to study it qualitatively in the whole phase plane.
PACS number(s): 04.20.Jb