Total mass of a patch of a matter-dominated Friedmann-Robertson-Walker universe

Abstract

In this thesis, I have addressed the question of how to calculate the total relativistic mass for a patch of a spherically-symmetric matter-dominated spacetime of negative curvature. This calculation provides the open-universe analogue to a similar calculation first proposed by Zel'dovich in 1962. I consider a finite, spherically-symmetric (SO(3)) spatial region of a Friedmann-Robertson-Walker (FRW) universe surrounded with a vacuum described by the Schwarzschild metric. Provided that the patch of FRW spacetime is glued along its boundary to a Schwarzschild spacetime in a sufficiently smooth manner, the result is a spatial region of FRW which transitions smoothly to an asymptotically flat exterior region such that spherical symmetry is preserved throughout. I demonstrate that this mass diverges as the size of the patch is taken to include the entire universe, and discuss the intuition provided by a classical approximation to the total mass using the formalism of Newtonian Cosmology.