Noether Symmetries of Lemaitre-Tolman-Bondi Metric via Rif Tree Approach

Abstract

In this paper, we have explored Noether symmetries for the Lagrangian corresponding to the Lemaitre-Tolman-Bondi (LTB) spacetime metric via a Rif tree approach. Instead of the frequently used method of directly integrating the Noether symmetry equations, a MAPLE algorithm is used to convert these equations to the reduced involutive form (Rif). The interesting feature of this algorithm is that it provides all possible metrics admitting different dimensional Noether symmetries. These metrics are given in the form of branches of a tree, known as a Rif tree. These metrics are used to solve the determining equations and the explicit form of symmetry vector fields are found, giving 4, 5, 6, 7, 8, 9, 11, and 17-dimensional Noether algebras. To add some physical implications, Einstein’s field equations are used to find the stress-energy tensor for all the explicitly known metrics, and the parameters appearing in the metrics are used to find bounds for different energy conditions.