Isometric group of $(α,β)$-type Finsler space and the symmetry of Very Special Relativity

Details Isometric group of $(α,β)$-type Finsler space and the symmetry of Very Special Relativity Isometric group of $(α,β)$-type Finsler space and the symmetry of Very Special Relativity

2010-01-15

arxiv.org/abs/1001.2667v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

The Killing equation for a general Finsler space is set up. It is showed that the Killing equation of $(\alpha,\beta)$ space can be divided into two parts. One is the same with Killing equation of a Riemannian metric, another equation can be regarded as a constraint. The solutions of Killing equations present explicitly the isometric symmetry of Finsler space. We find that the isometric group of a special case of $(\alpha,\beta)$ space is the same with the symmetry of Very Special Relativity (VSR). The Killing vectors of Finsler-Funk space are given. Unlike Riemannian constant curvature space, the 4 dimensional Funk space with constant curvature just have 6 independent Killing vectors.

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