The field of normals and comoving coordinates
The field of normals and comoving coordinates. Ruslan A. Sharipov 1 ... 4 5 6 ... ru In the new theory, which is called the 3D-brane universe model, there is a special infinite family of 3D-branes (see 3D-branes in thespace-time ). It turns spacetime into a 3D brane foliation. Each brane in this foliation corresponds to a specific instant in the evolution of the universe. Only one of the branes corresponds to the current instant, that is, the instant of the present. It is that very brane that has the prototype in the form of the real three-dimensional physical universe in its current state. The remaining branes correspond to past states of the universe that have ceased to exist, and its future states that have not yet formed. Let us choose at each point of each 3D-brane the vector of unit length perpendicular to the brane and directed towards the future. Such vectors form the vector field of unit normal vectors to the branes. Each vector field has integral c