ON THE QUALITATIVE ANALYSIS OF SOME STATIC CYLINDRICALLY SYMMETRIC SOLUTIONS OF THE EINSTEIN EQUATIONS

摘要

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.