The Behavior of a Spherical Hole in an Infinite Uniform Universe
  In this paper, the behavior of a spherical hole in an otherwise infinite and uniform universe is investigated. First, the Newtonian theory is developed. The concept of negative gravity, an outward gravitational force acting away from the center of the spherical hole, is presented, and the resulting expansion of the hole is investigated. Then, the same result is derived using the techniques of Einstein's theory of general relativity. The field equations are solved for an infinite uniform universe and then for an infinite universe in which matter is uniformly distributed except for a spherical hole. Negative pressure caused by negative gravity is utilized. The physical significance of the cosmological constant is explained, and a new physical concept, that of the gravitational potential of a hole, is discussed. The relationship between the Newtonian potential for a hole and the Schwarzschild solution of the field equations is explored. Finally, the geodesic equations are considered. It is shown that photons and particles are deflected away from the hole. An application of this idea is pursued, in which a new cosmology based upon expanding holes in a uniform universe is developed. The microwave background radiation and Hubble's Law, among others, are explained. Finally, current astronomical data are used to compute a remarkably accurate value of Hubble's constant, as well as estimates of the average mass density of the universe and the cosmological constant. 
Gilbert N. Lewis (Michigan Technological University, Houghton,   Michigan and Richard N. Lewis)