Abstract
Using a 3-dimensional formulation of general relativity for non-empty spacetimes admitting a non-null Killing field, a transformation for generating new non-vacuum solutions of Einstein’s equations and its specialization to perfect-fluid configurations is presented. Assuming that the twist of the Killing field is a gradient, it is shown that the transformation can be applied to generate possibly new perfect-fluid solutions only when a strong restriction on the equation of state is imposed (i.e. ρ +3 P =0o rρ = P )or, alternatively, for the case of static spacetimes. Furthermore, the relation of the described technique to some previously known methods is given. In order to study the effect of this transformation, its application to known perfect-fluid solutions is presented. In this way, different previously known solutions can be written in a singe compact form.
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