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