# Accession Number:

## AD0618761

# Title:

## LOCAL IRREGULARITIES IN AN EXPANDING UNIVERSE,

# Descriptive Note:

# Corporate Author:

## HARVARD COLL OBSERVATORY CAMBRIDGE MASS

# Personal Author(s):

# Report Date:

## 1964-09-18

# Pagination or Media Count:

## 27.0

# Abstract:

Einsteins theory of gravitation is here applied to a model of the universe in which local irregularities in the space-time metric are superimposed on the values appropriate to a uniform, isotropic universe. The mass tensor is taken to be that of a perfect fluid. The mass density is considered to fluctuate about a mean D, the density in the uniform model, but the fluctuations need not be small with respect to D. The effect of pressure is included. The system of simultaneous equations derived by Lanczos in 1925, which relates the irregularities in the metric to the irregularities in the mass tensor, is shown to simplify under conditions of astronomical interest. The equation of motion for the irregularities is derived in comoving coordinates. The relation of the local inertial coordinate system to the comoving system is examined. The equation of motion in the inertial system is derived. Its validity is not restricted to small pressures. The inclusion of steady-state cosmology within general relativity appears to lead to inadmissible results when local irregularities are present.