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arXiv · 1609.02677

Killing Symmetry on Finsler Manifold

Takayoshi Ootsuka·Ryoko Yahagi·Muneyuki Ishida
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Abstract

Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\delta K^\flat =0$ by using the Killing non-linear 1-form $K^\flat$ and the spray operator $\delta$ with the Finsler non-linear connection. $K^\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $\delta K^\flat =0$ 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.

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Takayoshi Ootsuka, Ryoko Yahagi, Muneyuki Ishida. 2016-09-09. Killing Symmetry on Finsler Manifold. https://doi.org/10.1088/1361-6382/aa64b1

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