Abstract
A new class of exact solutions of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. The class of solutions is invariantly characterized by means of the following properties: (i) The energy-momentum tensor describes a perfect fluid. (ii) There are two commuting Killing vectors ξ andη which form an abelian groupG2 of motion. (iii) There is a timelike Killing vector parallel to the four-velocity of the fluid (rigid rotation of the fluid). (iv) The four-vector of the angular velocity of the fluid is a gradientΩi=−(1/4c)ɛirklUl (Ur:k−Uk:r)=χ′i. The last assumption is the reason that all solutions of this class can be found by solving an ordinary differential equation of the second order.
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