On the invariance properties of Vaidya-Bonner geodesics via symmetry operators

TL;DR

This paper analyzes the symmetry properties of Vaidya-Bonner geodesics using Noether and Lie point symmetries, classifying subalgebras and applying the analysis to specific cases.

Contribution

It provides a classification of symmetry subalgebras for Vaidya-Bonner geodesics and demonstrates their invariance properties through illustrative examples.

Findings

Classification of one-dimensional subalgebras of symmetries

Identification of optimal symmetry subalgebras

Application to specific Vaidya-Bonner cases

Abstract

In the present paper, we try to investigate the Noether symmetries and Lie point symmetries of the Vaidya-Bonner geodesics. Classification of one-dimensional subalgebras of Lie point symmetries are considered. In fact, the collection of pairwise non-conjugate one-dimensional subalgebras that are called the optimal system of subalgebras is determined. Moreover, as illustrative examples, the symmetry analysis is implemented on two special cases of the system.