Symmetries of geodesic motion in Gödel-type spacetimes

Abstract

In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of Gödel-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for $\dot{t},\dot{r},\dot{\varphi }$ and $\dot{z}$ of each classes I-IV which depends essentially on two independent parameters $m$ and $w$, we explicitly integrated the geodesic equations of motion for the corresponding Gödel-type spacetimes.

21 pages, minor revision, submitted to JCAP

References in corpus (5)

• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Using the Noether symmetry approach to probe the nature of dark energy
• Lie and Noether symmetries of geodesic equations and collineations
• Scalar Tensor Teleparallel Dark Gravity via Noether Symmetry
• The lightcone of Gödel-like spacetimes

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• Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes
• Approximate Noether gauge symmetries of Bardeen model
• Noether Symmetries and Some Exact Solutions in $f(R,T^2)$ Theory
• Noether Symmetries and Anisotropic Universe in Energy-Momentum Squared Gravity
• Physical Significance of Noether Symmetries
• Classification of the Lie and Noether symmetries for the Klein-Gordon equation in Anisotropic Cosmology
• Integration of the geodesic equations via Noether Symmetries
• Noether symmetries of the minimal surface Lagrangian for Gödel-type spacetimes