DYNAMICS OF GRAVITATIONAL-INSTABILITY IS NONLOCAL

Few recent generations of cosmologists have solved nonlocal Newtonian basic equations which describe the gravitational instability in an expanding universe. The general picture emerging from this approach is that the structure begins to form with the pancaking and then looks like a complicated hierarchical clustering and pancaking over a vast range of scales. In general relativity (GR) the equations of cosmological gravitational instability contain the electric part of the Weyl tenser represented by the local terms, and the magnetic part, represented by both local and nonlocal terms. If the magnetic part is ignored, then the Newtonian limit of the GR version of the basic equations without the magnetic part consists of the closed set of the local Lagrangian equations. Recently, this fact has drawn much attention, since the gravitational instability in that form would greatly simplify the study of cosmic structure formation. In particular, the filamentary structure of collapsing is predicted. In this paper we resolve the contradiction between the Newtonian theory and GR versions adopted in some recent papers. We show that dropping the magnetic part from the basic relativistic equations is incorrect. The correct Newtonian limit is derived by the lie-expansion of the GR equations and the Bianchi identities for the Weyl tenser. The last ones begin with similar to 1/c(3) order, therefore in this case one must take into account the magnetic part in the first nonvanishing post Newtonian order similar to 1/c(3), which contains nonlocal terms, unrelated to the gravitational waves, but directly related to the nonlocal gravitational interaction. For the first time we rigorously show that the basic GR equations with the magnetic part are reduced precisely to the canonic Newtonian nonlocal equations. Thus, the correct treatment of the relativistic version of the gravitational instability resurrects the canonic picture of the structure formation, where pancaking is the predominant form of collapsing in the single stream regime.