SUPERLUMINAL NON-BARYONIC PARTICLES IN A 3D-BRANE UNIVERSE WITHOUT EQUIDISTANCE POSTULATE. Ruslan Sharipov Abstract. The 3D-brane universe model is an alternative non-Einsteinian theory of gravity. The initial version of this theory uses the so-called equidistance postulate. In the current second version of the theory this postulate is omitted. In the present paper non-baryonic particles are studied within the second version of the theory. As an example their revolution around a Schwarzschild black hole is considered. 1. Introduction. The initial version of the 3D-brane universe model was built in the series of papers [1–6] (see also [7–11]). Its second version was started in [12]. In this version of the theory the gravitational field is described by a time-dependent 3D metric g ij = g ij (t, x 1 ,x 2 ,x 3 ), 1  i, j  3, (1.1) and by a time-dependent scalar function g 00 = g 00 (t, x 1 ,x 2 ,x 3 ). (1.2) Here x 1 ,x 2 ,x 3 are comoving coordinates. Their definition in the standard cosmo- logy can be found in [13]. In the 3D-brane universe model they are defined in [1] and [12]. Their definition is the same for both versions of the theory. Through t in (1.1) and (1.2) we denote the so-called brane time. It is well-defined in the first version of the theory due to the following equidistance postulate. Postulate 1.1. Watches of any two comoving observers can be synchronized. Comoving observers are those observers whose comoving coordinates are constants: x 1 (t) = const, x 2 (t) = const, x 3 (t) = const . In the initial version of the theory the brane time was defined as the proper time of any comoving observer. This definition was consistent due to the equidistance postulate 1.1. The equidistance postulate is excluded from the current version of the theory. Therefore the brane time is defined as the proper time of some particular 2010 Mathematics Subject Classification. 83D05, 83F05, 70H03, 53B50. Key words and phrases. superluminal motion, non-baryonic matter, 3D-brane universe. Typeset by A M S-T E X