A New Approach to Study the Lie and Noether Symmetries of Spacetimes

The main focus of this study is to revisit and investigate Lie and Noether symmetries (NS) admitted by some specific spacetimes of interest in general Relativity. These symmetries are of pivotal interest because their existence is directly related to the existence of conservation laws. Our emphasis in the present work is to use an algebraic approach (RIF tree type) to classify the differential constraints under which these symmetries are admitted and discuss their physical implications. We hope that the RIF tree approach will provide some additional cases not obtained previously.