Stationary axisymmetric perfect fluid solutions in general relativity |
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Authors: | Eduard Herlt |
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Affiliation: | (1) Wissenschaftsbereich Relativistische Physik, Sektion Physik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, DDR-6900 Jena, Germany |
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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 and 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 gradienti=–(1/4c)irklUl (Ur:k–Uk:r)=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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