Einstein's vacuum field equation: Painleve analysis and Lie symmetries

The current study deals with investigation of Einstein's vacuum field equation for exploring movable critical points. We employ first the Painleve analysis, and then we use the auto-Backlund transformation. Moreover, the Lie classical method will be implemented to obtain similarity reductions and exact solutions via discovering the entire sets of point symmetries. We show that symmetries of Einstein's vacuum field equation form an infinite-dimensional Lie algebra and arbitrary function f ( t ) in acquired solutions. In addition, various other arbitrary parameters provide enough freedom to simulate physical situations governed by this equation are observed.

Automated summary

This study investigates Einstein's vacuum field equation through Painleve analysis and auto-Backlund transformation, aiming to explore movable critical points and point symmetries. The results reveal that the symmetries of the equation form an infinite-dimensional Lie algebra, with acquired solutions containing arbitrary functions and parameters.