Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-10-11
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12pages, minor corrections
Scientific paper
Within the framework of projective geometry, we investigate kinematics and symmetry in $(\alpha,\beta)$ spacetime-one special types of Finsler spacetime. The projectively flat $(\alpha,\beta)$ spacetime with constant flag curvature is divided into four types. The symmetry in type A-Riemann spacetime with constant sectional curvature is just the one in de Sitter special relativity. The symmetry in type B-locally Minkowski spacetime is just the one in very special relativity. It is found that type C-Funk spacetime and type D-scaled Berwald's metric spacetime both possess the Lorentz group as its isometric group. The geodesic equation, algebra and dispersion relation in the $(\alpha,\beta)$ spacetime are given. The corresponding invariant special relativity in the four types of $(\alpha,\beta)$ spacetime contain two parameters-the speed of light and a geometrical parameter which may relate to the new physical scale. They all reduce to Einstein's special relativity while the geometrical parameter vanishes.
Chang Zhe
Li Xin
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