The spacetime structure of MOND with Tully-Fisher relation and Lorentz invariance violation

It is believed that the modification of Newtonian dynamics (MOND) is possible alternate for dark matter hypothesis. Although Bekenstein's TeVeS supplies a relativistic version of MOND, one may still wish a more concise covariant formulism of MOND. In this paper, within covariant geometrical framwork, we present another version of MOND. We show the spacetime structure of MOND with properties of Tully-Fisher relation and Lorentz invariance violation.