Spacetime structure of MOND with Tully-fisher relation and lorentz invariance violation

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