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Bäcklund Transformations of Einstein's Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid

E. Kyriakopoulos
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Abstract

Clairin's method of obtaining Bäcklund 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 Bäcklund transformations, while if $μ+ 3p =0$ it gives the transformation of Ehlers.

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E. Kyriakopoulos. 2001-02-06. Bäcklund Transformations of Einstein's Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid. https://arxiv.org/abs/gr-qc/0102021

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