Abstract
This paper is devoted to the study of approximate Lie point symmetries of general autoparallel systems. The significance of such systems is that they characterize the equations of motion of a Riemannian space under an affine parametrization. In particular, we formulate the first-order symmetry determining equations based on geometric requirements and stipulate that the underlying Riemannian space be approximate in nature. Lastly, we exemplify the results by application to some approximate wave-like manifolds.
Highlights
In a n-dimensional Riemannian space, it is a formidable task to compute the Lie point symmetries of any equation in that space, and this problem is only exacerbated if such an equation possesses a small perturbation
The objective of this work was to formalize the computation of approximate Lie point symmetries of autoparallel systems under a generic Riemannian space up to the first order in the perturbation parameter ε
We set up explicit geometric equations that, when solved, provide the approximate symmetries of the autoparallel systems
Summary
In a n-dimensional Riemannian space, it is a formidable task to compute the Lie point symmetries of any equation in that space, and this problem is only exacerbated if such an equation possesses a small perturbation. An additional point to note is that if it vanishes, the autoparallel system is affinely parameterized with the so-called affine parameter In this case, the autoparallels are the geodesics of the Riemannian space. We aim to apply the results of approximate Lie point symmetries to perturbative autoparallels and generalize it in an approximate Riemannian space. We will establish a geometric way of dealing with the autoparallel symmetry problem for the first-order perturbative Riemannian spaces. While many authors have studied approximate symmetries of geodesic equations, none have explored how to generalize the construction of these symmetries, the novelty of this work.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
