Lie and Noether symmetries of geodesic equations and collineations

Details Lie and Noether symmetries of geodesic equations and collineations Lie and Noether symmetries of geodesic equations and collineations

2011-01-30

arxiv.org/abs/1101.5769v1

General Relativity and Gravitation Volume 42, Number 12, 2957-2980, 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages

Scientific paper

10.1007/s10714-010-1054-9

The Lie symmetries of the geodesic equations in a Riemannian space are computed in terms of the special projective group and its degenerates (affine vectors, homothetic vector and Killing vectors) of the metric. The Noether symmetries of the same equations are given in terms of the homothetic and the Killing vectors of the metric. It is shown that the geodesic equations in a Riemannian space admit three linear first integrals and two quadratic first integrals. We apply the results in the case of Einstein spaces, the Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each case the Lie and the Noether symmetries are computed explicitly together with the corresponding linear and quadratic first integrals.

Affiliated with

Also associated with

No associations

Rating

Lie and Noether symmetries of geodesic equations and collineations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lie and Noether symmetries of geodesic equations and collineations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lie and Noether symmetries of geodesic equations and collineations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-157835