Planar numerical cosmology. I. The differential equations

This paper is the first in a series describing a method for evolving planar cosmological models on a computer. In this paper we set forth our coordinate conditions and variables, and discuss the way our special gauge simplifies the numerical evolution. We write down the Einstein equations that govern the gravitational field in our cosmologies, as well as the hydrodynamical equations for the fluid souces. Later papers in this series will present the differencing of these equations, tests of the code, and evolutions of dynamical inhomogeneous cosmological models. 25 references