Killing Symmetry on Finsler Manifold

Abstract

Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\delta K^{♭}=0$ by using the Killing non-linear 1-form $K^{♭}$ and the spray operator $\delta$ with the Finsler non-linear connection. $K^{♭}$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $\delta K^{♭}=0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian gravity.

12 pages

References in corpus (5)

• General Very Special Relativity is Finsler Geometry
• Deformed relativity symmetries and the local structure of spacetime
• Spacetime and observer space symmetries in the language of Cartan geometry
• Variational principle of relativistic perfect fluid
• Application of Kawaguchi Lagrangian formulation to string theory

Cited by in corpus (3)

• On Finsler spacetimes with a timelike Killing vector field
• Applications of the Schwarzschild-Finsler-Randers model
• Generalized Mathisson-Papapetrou-Tulczyjew-Dixon Equations