Behavior of Irregularities in the Distribution of Matter: Newtonian Approximation

Abstract

This chapter examines the behavior of a given mass distribution in the Newtonian approximation. Discussion of how irregularities in the matter distribution behave in an expanding universe is greatly simplified by the fact that a limiting approximation of general relativity, Newtonian mechanics, applies in a region small compared to the Hubble length. The rest of the universe can affect the region only through a tidal field. Though the point was clearly made by Georges Lemaître, it has not always been recognized that the Newtonian approximation is not a model but a limiting case valid no matter what is happening in the distant parts of the universe. Because of the importance of this result, the chapter discusses it at some length.