EXACT SOLUTIONS OF EINSTEIN'S FIELD EQUATION
Springer Online Journal Archives 1860-2000
Abstract We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect-fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a “seed” solution of the Einstein-perfect-fluid equations with a Killing vector. The seed solution must either have (i) a spacelike Killing vector and equation of state P = ρ or (ii) a timelike Killing vector and equation of state ρ + 3P = 0. The new solution generated by this technique then has the same Killing vector and the same equation of state. We choose several simple seed solutions with these equations of state and where the Killing vector has no twist. The new solutions are twisting versions of the seed solutions.
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