B\"acklund Transformations of Einstein's Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid
Abstract
Clairin's method of obtaining B\"acklund transformations is applied to Einstein's field equations for the interior of a uniformly rotating stationary axisymmetric perfect fluid. It is shown that for arbitrary pressure p and mass density μ the method does not give non-trivial B\"acklund transformations, while if μ + 3p =0 it gives the transformation of Ehlers.
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